Amplifiers.

You can buy a 1W Marshall for $35 - guaranteed not to annoy the parents!

http://www.samedaymusic.com/product--MSHMS2

/edit: I've got one and it's not bad - just not very loud!

Whoops...I could have been a little clearer, huh?

If you don't mind the fact that nobody else will be able to hear you (unless you let them borrow your headphones or plug into something with speakers), the headphone amps are great choices. Almost all of them have things like "amp and speaker simulators" which make it sound like you're playing through much more expensive equipment, and you can wail to your heart's content in the middle of the night even with people sleeping a few feet away. And if you stick with the guitar, a good headphone amp can still be useful later on...whereas you'll probably outgrow a little practice amp pretty quickly.

The ones I've liked are the Line6 POD (the new ones are probably over your price range, but used ones are much cheaper and there's thousands of them on eBay, for instance), and the Johnson J-station (used, under $100 US).

There's also the Korg Pandora: they have a few different models..the newest is the PX4...the PX3 is a year older but still very cool and probably right around your spending limit, and the older PX2 is even cheaper...probably about half of what you're willing to spend.

And Zoom has the 505II which is even cheaper (around $50-60 US) and will definitely do the job.

But if you don't want to wear headphones to hear yourself play, I recommend the Line6 Spider II practice amp. It's right on the edge of your price range, but it's got good sounds at any volume and a headphone jack (just in case it's still not quiet enough to keep the parents happy).

Maybe it's not what you're looking for, but I highly recommend getting a pair of headphones and a modelling unit instead of a practice amp. I use the Line6 POD almost exclusively, but the Johnson J-station is great too- they're discontinued now, so you can get one for under $100 with a little searching. There's a lot of other inexpensive choices...I know a lot of people who love their Korg Pandora, for instance.

They're more versatile and sound better than any practice amp at a comparable price. Plus, if you do eventually get into a performing situation, you can pick up a power amp and a cabinet and still keep the sounds you like. I know for a fact that the POD sounds better than most amps when it's run through a 4x12" cab.