I'm mostly looking to get the most out of my music on my computer. I do plenty of gaming, but audio for that isn't really a priority. I listen to a little rap and electronic, but not enough that bass is super important; mostly metal and hardcore
Personally, I favor enough amplification for the task at hand, maybe a little more. Music will sound a good deal more dynamic when your amp has enough power to support ample headroom, instead of clipping or running flat on musical peaks.
One other consideration for amps is space. If you're looking for a small desktop unit, that rules out a lot of vintage gear, one reason you see so much from the 80's and 90's up for sale is because they run large. However, if you've got a spare side table, you can set up a really nice system for both music listening as well as gaming support. Although you didn't mention listening to radio or CDs, I wouldn't rule out an integrated amp/receiver, there are some real bargains in that category, priced well under your budget target.