In general, second-hand cars are as reliable as you make them. Hondas are sort of an exception; for whatever reason, they just don't mind abuse. A BMW as a first car's a really good idea if you get the right one, because it's a virtual certainty that you'll love driving it and everyone else will think you're the man. However, if you buy one that hasn't been taken care of in terms of maintenance, they you'll either have to face spending a lot of money on OEM replacement parts and resume the first scenario or try to do what we kids do, go to AutoZone and put whatever they've got on there, and have it break a year or two later and do it again.
Personally, I think that ten grand for a high school student is astounding, no matter where you spend it. You can get an E36 for less than that, sure, but you're going to get one with a few miles (not too big a deal if it's been kept up) and you probably won't get the most fun features, like the big engine or immaculate paint. I think it might benefit you more to sock half of that money away for college/BMW #2/whatever, and spend five thousand on an E30 3-series or E34 5. Either of those cars will be plenty reliable and fun for a first car, and shouldn't need more than a few hundred dollars of TLC.
It's up to you what you want to do with that cash, either spend a portion of it on buying and restoring an older car, or buy a newer one and hope nothing too expensive breaks. Some of the more common E36 problems and fixes are listed here
. If you want to go check some out and see just what kind of shape they're in for your price range, here's a list of what to look for
. And also, if you decide that you want to try and work some of its issues out yourself, there are several do-it-yourself articles
for the E36.
Finally, welcome to the forums! If you wind up getting a BMW, stick around, there are a lot of really helpful people here. Let us know how it goes!