The Beamers are affordable and their motors are reasonably reliable, but they've got too many other problems and are generally too pricy to maintain to fit the criteria this guy's looking for.
Here is a short list of cars I would consider if I were in your position.
1. Infiniti G35 (Sedan or Coupe): 03s can be had for under $11k. A little pricy, but arguably the best bang for the buck in its class.
2. Acura RSX: Easy to find an 02-05 in your range and well below it (sub $8k). Small, sporty coupe popular among young guys. Very reliable, good value.
3. Acura TSX: More mature alternative to the RSX. Small sedan based on the Japanese/European version of the Accord. You can find 04's for $10k or less, though if you can stretch a little ($11K) there are more options.
4. Acura TL: The older ones (01-03) are easy to find for south of $10k. For sportiness, shoot for a Type S. Very affordable, super reliable, luxurious (you'll get your leather, sunroof, etc) and cheap.
You can find some newer ones (04's) in this range, but prepare for higher mileage. They're reliable, though, so whether or not you want to deal with that is up to you.
5. Honda Civic Si: 02-06 models are available in this range. Small coupe/hatchback, good mileage, popular young guy car.
6. Lexus IS300: 01-03, small sporty sedan. Great value, extremely well put together. Not as sharp on the track as the E46 3-Series, but fewer expensive bugs in other areas. Highly recommended-I wanted one of these myself, but financially couldn't make it work.
7. Mitsubishi Eclipse: 02-07, these things depreciated like mad, which makes them easy to find for under $10k. Not terribly exciting, but they look sporty enough and will get you reliably from A to B.
8. Toyota Celica: Another sporty coupe like the Eclipse, though it is smaller and a little sportier. 01-04's are abundant for under $10k. I'd recommend the Celica ahead of the Eclipse, actually.