328i sedan + turbo kit + suspension < $10k
Here's one with higher mileage but I've driven it numerous times and it's a SOLID car.
$4,600 http://atlanta.craigslist.org/cto/989480866.html
I'm sure the current owner would do a turbo setup on it for around the $10k budget as well. There's a few '97+ for around $5-6k but there is no way they have the service, maintenance, and upgrades the above one has.
A 400whp e36 sedan with upgraded suspension would eat most sports cars for breakfast. The M3's are nice but higher insurance and more expensive parts. The 328's M52 takes boost alot better than the S50/52 from an M3 as well due to having more meat between the cylinders.