B13 SE-R, you can find between $2000 and $500

...going price for a ratty one with body rust but intact engine and mechanicals would be $1000, I'd guess.
It'd be way faster than an equally ratty carburated Z31. Low seven-second car. Buy a semi-rustless one for $1,500, fix it up for another $500... find a buddy who's good with wrenches and slap in an SR20DET for another $2.5k... and you've got a 13-second street car that'll eat clutches for breakfast, drive-axles for lunch and gears for dessert.
The great thing about the car, though, is no matter how crappy it'll look on the outside or how many miles on the odometer, the SR20DE engine will still probably be working, and will still probably be making full power and will still rev to 7k rpms. Buy a late model SE-R (B15, 2.5 liter), and it's a crapshoot as to whether it's the year model where the engine ate its own catalytic converter and stopped working, or the year model where the engine just stopped working, period.
Great car. Spend the rest of your budget sorting the suspension instead of buying an expensive turbo, and you've got a great car to learn track-driving on, too.
I don't know what the going rate is on a B14 SE-R (or was it 200SX?). It's slower in a straight line, but the chassis is much better (even with the rear beam axle and the sort of dead steering), and it was even available in 4-door SE-L. Tracksters love this car, and it'll dice it up with faster machinery with the right modifications. The B15 still came with the SR20 engine, but by that time, emissions and weight had strangled almost all of the performance out of it, and it needed the QR25 to get moving.