If you're using them inside, I'd say the Grado SR's are a very good place to start. SR125 would be at the lower range of your budget, SR225 (which I have) at the upper end. Yes they look hokey, but as the salesguy said to me, "they sound as good as they look sh!t"
The 125's would probably be just the right phones for you. In the short time I compared the two, I decided on the 225 because it sounded easier to casually listen to.
One potential problem with the Grados is that they are very open - which means that they let a lot of ambient noise in. If you live in a noisy household, this may be a problem.
Another 'open' phone which gets consistent mentions of 'bass' and generally good reviews is the Sennheiser HD580. I can't comment on it, but this is definitely one phone to try.
The alternative is 'closed' phones. These are closed against ambient noise intrusion. However this process colors the sound slightly.
The Sennheiser HD280 is one closed phone often recommended here. I unfortunately can't recommend the Sennheiser HD280 for all sorts of reasons - lack of comfort, over-emphasis on the trebles (although you can defeat this with the graphic equalizer), etc. Annoying to listen to in the end, if that's all you're doing - listening that is, not analysing the music.
Give them a try by all means if you can since many of the seemingly more geeky contingent here like them - but do not buy these phones untried. If you do try them in a shop, and the phones are new, bear in mind that bass response improves after a while on these phones - but not by a spectacular amount.
The Sennheiser has one thing going for it though - which is the fact that they let very little ambient noise in. I have the 280 and have relegated it to computer headphone duty.
Well, no, relegate is too strong a word - they're superb headphones for certain music, classical and soft rock for example - but not really your dancy headphones. Due to their isolation they also do work very, very well as a computer phone BTW, especially if you have several PC's in a room as I do.
After a lot of research, I've recently ordered an Audio-Technica ATH-A9X. If you don't like the look of the Grados, I think you might like this for your musical tastes. I ordered mine from a shop, but you can get it from audiocubes.com - at $189.