So you may be able to find a reasonably priced apartment in a transitioning neighborhood of DC. Otherwise, your best bets are probably in one of these neighborhoods: College Park, Greenbelt, Adelphi, Berwyn Heights, Riverdale. None of these neighborhoods are great, but they are a fine place for a college student to crash. I would recommend a complex, but the ones I've been to aren't worth your time. I've heard that Greenbelt proper (look for Greenbelt in Google Maps, it's just east of Buddy Attick lake) is the nicest neighborhood in the area, with apartments available from owners of the historic houses there. Points of advice:
Check apartmentratings.com - the reviews there are reasonably accurate. I've used them to make renting decisions before and have left reviews there.
Check Craigslist for apartments in houses (this is the best value, and potentially the most enjoyable experience).
Make sure you're near a ShuttleUM stop. This would be preferable to the DC Metro Bus.