Ooh, it seems to me what you need is a pair of AKG k271S's! They're closed, they have a beautiful, natural midrange, and they have lovely replaceable pleather pads (I guess you could clean them too .. haven't tried that). They're also good-lookin' and robust, so I wouldn't worry about them getting dirty. Retail price is $200 (even that is within your budget), but you can get them for around $150.
Some people say their bass is a little weak and I agreed when I first got them, but it really opens up over time (I used to give them an EQ bass boost, but after having them for about a month I turned it off and it sounded the same!) However, if you think you want a little more bass than the average Joe, you could go with the AKG k240, the 271's "semi-closed" (less isolation than the 271) and semi-priced cousin. It supposedly has quite a bit of bass (though not as tight and defined as the 271), but other than that they are said to be quite similar (I've never heard them).
Hope that helps!
EDIT: Oh yeah, as for the remaining allotted funds, either save up for a good amp (i.e. Gilmore Lite @ $350), or spend $50 of it and get a small amp (i.e. Go-Vibe, PocketAmp, or CMoy).