How far away will you be sitting? I just ask as I couldn't go with anything smaller than 50", but I can see 37" being ok if it's a small room (dorm etc.) and you'll be sitting very close.
I bought a 50" Sony LCD RPTV last summer for $999.99 so bigger sizes are possible in your budget.
For a 37" I'd say go with a decent LCD TV from Sony, Sharp etc. if you can find one in that price range, or save up. I wouldn't go cheap and get a Westinghouse, Vizio etc. You get what you pay for. I first bought a 42" Vizio Plasma last summer and ended up returning it as it made loud buzzing noises and their technician couldn't fix it (said it was just a typical problem of that model).