Get a used E36 M3 for ~$15,000.
BMW's are amazing cars. I just recently bought a '94 325is, one of the best cars I've ever driven especially for $4800. My dad owns a modded '02 337 GTi and he told me flat out he likes the feeling of my car better than his, and if he could buy one new he would in a heartbeat. Some of the IS models came with a limited slip, they aren't hard to find. They were all lowered from the factory with front & rear swaybars, in addition to near perfect 50/50 weight distribution.
Keep in mind:
My car is only chipped w/ freeflow exhaust @ ~210hp,
Dad's car has been chipped @ 18# of boost, lowered with sport springs, front and rear sways w/ strut tower braces, catback exhaust, urethane suspension bushings, motor mounts and transmission mounts, 13# flywheel with stronger clutch, short shift kit and high output coil packs - he estimates in the region of 240-260hp.
That thing is damn fast and handles on rails, and he chooses the 13yr old bimmer. Mine's a 325, the m3 is to die for.