Sure you could get a nice BM for that amount; maybe an E30 325i Sport or a 325i Cab.
Either go for a standard one in mint condition and just enjoy it, or find one that someone else has done the hard and expensive work on, and that way you'll have some savings. Believe me, you'll need them to run any car and for those unforeseen things that can crop up!
I'm assuming you're younger as it's your first car. Is insurance for young drivers in the U.S. also sky high as in the UK and Europe?