Hi Gahpar, welcome! I'm a kybd player (among other things) and the absolute minimum basics I look for in a "prog friendly" synth are good Hammond organ sounds, at least 4 or 5 good lead synth sounds, a decent acoustic piano sound and most importantly for me, a synth that you can load mellotron samples into. This guy on ebay called "vintagekeyboardsounds.com" sells samples of an actual mellotron M400 for $20 in many synth formats...I'd check him out and see what sample formats he has and start looking for synth/samplers that support those. You'll probably also want a synth with some decent on-board effects processing (at least reverb and hopefully some delays) unless you plan to run your synth through effects pedals.
For all those features you'll likely be looking at what are called synth workstations. I play a Yamaha Motif XF-7 which does all this (and infinitely more) but is unfortunately way out of your price range. I know the Motif has a little brother called a MOX for about $1000, but don't know if it's also a sampler. If you don't care about mellotron, then a non sampler might be ok. Some non-samplers have voices they call "mellotron" but they're usually very poor attempts at capturing the magic of the real thing.
Happy hunting!