IMHO, here are your options:

For that price, you'll be lucky to find something in good shape, that hasn't been ragged out but it is doable...
1) 90 300zx TT
2) 1st or 2nd Gen DSM TURBO - Eclipse GST or GSX, Talon, or Laser, even the galant VR-4
3) 91 3000gt VR-4
4) MKIII Toyota Supra Turbo
5) 97 Prelude, quick enough, good looking, and very reliable. High mile automatics sell in the 5k range.
6) 91 Mr2 Turbo
7) 95 Integra GS-R
8) Subaru SVX - Kinda Quirky cars, very unique
9) SWAPPED 240 - good luck finding one at that price point that hasn't been wrapped around a tree and glued back together for 5k

At this price point, and you wanting something fast, most of these cars are gonna be 100k+ vehicles. Don't be afraid to get someone to drive you a few hundred miles to pick up the right car, instead of settling for something thats just ok local.

I think if it were me I would take my time and go for the right 90 Z TT, MR2, or 2nd Gen GST (as long as the transmission has been replaced). Something manual of course for me.

Just my .02

Let us know what you decide on.