Far better in my opinion, is to aspire to become a better all round musician.

It's not about how fast you can talk, but rather about what you have to say.

What I mostly want to do is melodic rock. Sorry for the cliche but Mr. Gilmour is my absolute favourite and influence. Though I don't want to be exactly the same, I'm not going to reach the same skill and being a copy isn't fun, but he's a big example for me. 

Therefore, I think point 4) is most important for me, but I'll definitely go through them all.

I got one question though: is it more useful to know a lot about chords or about scales? 

Though sometimes I think something I'm never sure of: for such (not too fast and) melodic solos, it's more the musical feeling than the technique/experience of playing.

In general: I'm not sure I'm able to go to a tutor. I just don't want to quit piano lessons and those two at the same time won't work.

Alright. Some tips.

1. Write parts you have trouble playing and play them with a click track or metronome. If you have trouble with them, play them slow. 

2. Come up with parts based on novel ideas that are idiomatic to the guitar. For instance, melodies using only harmonics. Not that that hasn't been done, but things like that help you think outside the box.

3. Stretch your improvising skills by putting some kind of limit on yourself. I did this subconsciously by starting on non-chord-tones and using as many I could just because I liked the sound. Think about limits you can place on yourself and come up with ideas in those limits.

4. Learn to play and sing at the same time. Being able to contextualize melodies with what you're playing on guitar can help your melodic ear.

5. Buy a loop station or find some way to do the following: Write a chord progression. Record and loop it. Play over it ad nauseam. Find licks you like over it. 

6. Remember that music is sound. As much as noodling and practicing unplugged by yourself helps. It helps to practice with an amp and also with other people. One thing about improvisation is that, in a band setting, it's very much about feeding off of people's ideas. If the drummer plays a triplet fill, you can play a triplet lick, or interact with it some other way. You can harmonize with the bassline. You can create crazy noises to match the energy of what the other band members are doing. 

7. Transcription. Transcribe solos, riffs, melodies, chord progressions from anything of any genre, even if it's not on guitar or guitar isn't even present in the recording. Film scores, jazz, classical, pop songs, whatever catches your ear. 

The main thing that made improvement very natural for me was that playing guitar was almost synonymous with writing songs from the outset. Before I learned any songs, I learned a few chords and arranged a chord progression out of them. I transcribed several different things (and developed good ears thereby) because I wanted to write songs with that mood or emotional resonance. I learned a good bit of theory along the way, so I knew many scale/mode names and the theory behind them, but I didn't practice scales as much as people might think because I listened to a good deal of music that was modal or in strange scales and wrote stuff based on the sound of those songs myself such that I eventually got a feel for how they laid on guitar and how to use the anyway. I wrote parts that were technically hard for me to play and improved my technique that way. I got into avant-garde music and wrote plenty of that and came back to tonal music with increased versatility. I listened to a lot of music (still do) and imitated things I heard.

But the experience I did have with one particular teacher was invaluable. My final tip: If you go looking for a teacher, look for a good jazz teacher. They'll usually have more tricks up their sleeve in terms of improvisation and soloing than a rock or classical one. (Just don't imitate their tendency to turn the tone knob all the way down ).

or, for more of a stretch,

11th fret on low E string, 10th fret on D string, 7th fret on G string, 8th fret on B string

or or  or with Eb

Still interested ? ;-)

I get 1001 people saying "I wish I could play the sax." Strangely, all of them have never actually bought a sax. I then offer to take them to a music shop, if they bring about a grand I can get them started on a good basic sax: they then just have to practice for the rest of their lives. No takers so far. ;-)

Both.  Gilmour is basically a blues guitarist, so learn Major and Minor chords, and the Blues scale, and you will be on your way.  

Most important thing is not to get frustrated, but since you are already a keyboardist, you should do OK.

Regarding learning guitar. 

I play sax, guitar, bass, flute and keyboards. Been playing 40 years. 

My best advice about learning a musical instrument is this: get an MP3 player. Immerse yourself in music of all tastes. Listen to the music, play along with it in your head and then on an instrument. After a LONG time, you will develop all the skills needed to improvise and will have an enormous back catalogue of ideas in your subconscious to call on. That's what takes a long time in becoming a musician. 

There are several stages. In the first stage, you are constrained by the physical limitations of learning to play the instrument. After you get over that, you are then constrained by an adherence to the music - ie., you've immersed yourself in tab and can't think without it, you have no ideas of your own. Throw the tab or sheet music away. Third stage. You begin to learn to improvise and this means a lot of time and mistakes. Fourth stage, you just play. An idea automatically pops up and comes out of the instrument. It takes quite some time to get there. 

Equipment.

Most novice musicians fall into the trap of trying to compensate for lack of skill by buying equipment. They simple must have guitar X, with capacitor Y's in it, they must use these strings, this amp and this tuner. Guitarists are especially prone to this. Truth be told, 95% of guitarists can't play beyond tab or strumming a few simple chords. Not many improvise. You can sit in a music shop all day and hear one or two people doing something new or novel. Pretty poor figures. Avoid music forums as much as you can, for example, the Moog one is just nasty and most guitar forums are full of unpleasant people telling you you must do this or that and that they're subtly better than you. NO amount of equipment is a substitute for skill.

Practice

Ginger Baker practices drums for 30 minutes a day. His argument is that musicians fall into the trap of overpractising one riff or beat. Scales are like times tables. Know them ? Stop practicing them, or you will fall into the trap of "scales go up and then down" - I've known people who just practice scales for 50 years.... C D E F G A B C / C B A G F E D C . They never learn anything at all. Do NOT rely on sheet music and realise that it's not the scale, the scale is just the framework. Really, it's the idea which drives the music, the scale and chord progression naturally follow. 

All musical theory is useful in the same way that higher mathematics is useful. You don't have time on stage, when improvising, to refer to music theory. An idea comes in your head, you play it. That's all that's required. Have a nodding relationship with theory but no amount of theory will make you a musician. Ditto sheet music. Sheet music is a representation of music, not music itself. It's like saying knowing the words in a book give you the ability to write a novel. Sheet music is seen as the be all and end all to a lot of musicians: they lean on it and tab like a crutch. Take the sheet music away, they can't play Baa Baa Black Sheep. Some musician. 

There are 1001 other things I could come up with but..... the most important one is NEVER play to be famous or rich or make money. Play for the music. If you don't play for the music, you will produce worthless crap. 

Finally, be yourself.

You could lock yourself in a room for 15 years and learn every single note Jimi Hendrix ever played. You could then go out and play them, oscilloscope perfect. And guess what ? You would produce nothing of any worth whatsoever. That makes you a guitar copyist and a fantasist, not a guitarist. 

One thing that is extremely annoying is my timing, it's crap. Over all the years that I've played piano and other instruments, I've played 85% totally solo (practicing at home mostly or on stage solo), 10% with other people (lots of different formations) and 5% "studio" (in my bedroom, but recording for songs that I make). Therefore I developed a timing which doesn't fit with a metronome. Let me make my point clear, if you hear a pianist playing Chopin, the tempo moves up and down whole the time, that's how it should kind of. Now, I don't want to record with a frustrating metronome in my ears (makes it to robotic and not "free" enough) but timing every instrument perfectly is almost undoable for me.

How can I fix this? Are there any tricks perhaps?

BTW, it's not any problem when playing "live" in a group, just recording over other self-recorded tracks.

It's really just about hard work and focus.

Recording to a regular pulse isn't 'boring', it's a skill that needs to be learnt, in the same way that playing outside of a fixed rhythm  has to be learnt in order to do it well.

Beginners make the mistake of learning to rely on the metronome, rather than listening to the music. You can't do both. The only time a metronome might come in useful is if you're playing without reference to any other instrument and need to keep time. Metronomes are made to be sold by companies to beginner musicians who think they need metronomes, as the company has told them they do. 

Keeping time with a band is an acquired skill. It comes with practice. Half listen to the drummer. Half listen to everything else. Feel the music and relax. 

Don't worry about being slightly off beat, file under "syncopation". Not everything - if you're a guitarist - has to be on beat. This is music, not precision engineering. 

The sticky out thing on your leg is a foot. Learn to tap it. That is an acceptable substitute. 

...truest statement ever made about learning an instrument.

Learning to playing the guitar really hurts, especially as your finger-tips haven't become hardened and calloused. In the beginning you'll find that the pain comes long before any fatigue so the important thing is not to be brave and fight through the pain as that can lead to blisters and cuts, even though the rest of your body wants to keep playing. Either of those two injuries can stop you playing for days while they heal and that puts you back to square-one when you start again. Therefore don't practice for long stretches but break them up into shorter periods with rest intervals to recover, four half-hour practices a day are better than a continuous two-hour one. 

And mine too. 

I asked a guitarist friend what was the best advice he was ever given and his reply was "keep tapping your foot"

I'm trying to practice most as I can, it seems better to just practice a lot than keep asking how to practice exactly. Although I've been playing for a while especially my hand on the fretboard hurts quite quickly, just a few bends and the skin wants to leave my finger...

Tapping with my feet is indeed probably way better, I tended to not use it at first; I find it distracting but probably I'll need to just get used to it. This might be actually the reason of my timing-problem!

Oh and by the way, I never used a metronome anyway (I wasn't clear I think).

Do you think it's best to first record every other instrument and then guitar?

There are no hard and fast rules here. Though usually rhythm tracks are recorded before any melody tracks, then lead and solos are recorded last. If your piece has rhythm guitar then record that early as it is a guide for everything else and acts as "a place-keeper" for verse, chorus and bridge sections.

As odd as it sounds the rhythm guitar is sometimes more useful as "the time-keeper" than the drum or bass so recording a rhythm guitar guide track before recording the drum track can be an advantage .. or having the rhythm guitarist play along while recording the drums (or bass) just to keep the drummer (or bassist) on course. If you are not using a real drummer then obviously that's unnecessary.

/edit:

If you get used to tapping on the beat with your feet, you feel the music much more than with a ticky-tick metronome. And it's all about feeling the music. 

It used to be that I could keep time with my right leg, but if I used my left, my timing was off. ;-)

As a PS yes, your fingers will initially hurt. This is normal. So go owwwww and feel that warm glow associated with doing that bit right. ;-) Good job you're bending strings. Lots of guitarists, sorry, "guitarists".... don't. They think they can get away without doing so. Uh uh. 

The point about learning an instrument is that there is a price to pay, whether in time, money or pain, to get to a certain point. You're paying in pain and some frustration at the moment. This, again, is normal. You'll find lots of musicians, sorry, "musicians" who expect there's some kind of magic short cut. This is like picking up a Japanese dictionary and thinking there's a magic way to learn to speak fluent Japanese in two weeks. Some magic formula which unlocks everything. Yeah, well. Right. ;-)

Dean is 100% right in that there are no hard and fast rules about how to record a song and in what order. It's whatever works, and that comes with experience, and occasionally, at 3 in the morning when you have the idea for a guitar riff, drum break, nose flute solo, whatever. It's all personal. I come up with a riff which drives a song or a chord progression which leads to ideas, or hear a drum pattern which starts something off, and it all goes from there. Don't worry about it, it sorts itself out. ;-) You'll notice there are composers' threads on this board - "how to do it" - and I don't subscribe to the idea that there is a set way to compose or record or play music, as that generally produces .... formulaic pieces. It's all about inspiration and intuition. That comes with practice and experience. 

Oh yes, really, there are no teachers for this kind of thing. There are people who can show you ideas and techniques, but the only person who will really teach you anything - by repetition, practice, trial and error.... is you. Most people think learning an instrument is a set task, you do A, you do B, you've learnt to play. It's not like that. It's an evolutionary process where you can go as deep or as shallow as you want to. But you WILL get there, with the correct attitude. And a lot of bloody minded determination. 

And good luck. ;-)

If you want to specifically learn how to solo on guitar, I would start with learning the pentatonic (or blues) scale.  It's a simple pattern (with a couple variations) that you can easily move anywhere on the neck to play in different keys.  And as the saying goes, playing blues guitar takes a minute to learn and a lifetime to master.  There are tons of examples on the net (just search for "pentatonic scale guitar") including youtube videos that will show you exactly how it works.  

Next, I'd suggest a program like Band-in-a-Box which is a wonderful learning tool.  You can easily setup your "backup band" to play a I-IV-V progression in seconds then use the pentatonic scale to solo over it until you eventually fall over from exhaustion   

The biggest thing that opened up the world of guitar soloing for me back in 1980 was when I bought a book and learned the pentatonic scale.  And just because it's known as a "blues" scale doesn't mean it's limited to the blues.  When you hear Gary Green or Steve Howe ripping those fantastic rocking solo's back in the 70's, the basis of those are the pentatonic scales.  Best of all, nowadays with the resources of the internet, you don't need a book and will find youtube ready and willing to be your guitar teacher any time of the day or night. 

Best of luck and rock on 

Everyone tends to use them, but the better the player, the less they use such cliches.

Go into any guitar shop on a Saturday and 90% of what you hear will be minor pentatonics.

It really depends on what feeling you're after.  If you want to remain rooted in one scale, you should try to choose a scale that encompasses the roots of the chords that will be changing underneath it.  For example, soloing in C major will sound pleasing over the C major diatonic chords (C, dm, em, F, G7, Am, Bdim, C - in other words the chords that are made up of strictly the notes of the C major scale) because the notes in C major all correspond to the roots-3rds-5ths-7ths of those chords.  In other words, every note you play in C major will somehow directly relate to the diatonic chords underneath.  Soloing in Am (or the more abbreviated A minor pentatonic scale) over those same chords will give you that rock/blues feel that is so pleasing.  Basically for the same reason, the notes in A minor pentatonic (or Am) all relate to the C major diatonic chords moving underneath but in a different twist.  You can also get really advanced in choosing a scale by incorporating modes, but that's a more advanced theory discussion.  Actually, playing the A minor pentatonic scale over C chords is playing the Aeolian mode so playing the blues is actually more theory literate than anyone imagined.  Zappa was known to play extended solos in the Lydian mode, often whether it was related to the chords underneath or not 

Simply put, just experiment!  Play, Play, Play!  That's why Band-in-a-Box is so great...you can quickly setup a chord progression that will repeat until Armageddon if you like, change it up...does the C major scale still work for you if you play it over C, F, and Gm?  If not, why?  Try the C pentatonic scale over a diatonic chord progression in F#.  Do you like it?  If not just slide your scale around until you find something that speaks to you.