GTI-R is a good choice. plus they look like a normal-ish hatch so you wont cop hassle from tha man.
I reckon you only have these choices:
GTI-R
SR20 S13
MX5
Any of them will be a good choice. GTI-R can be bought so cheaply now, and if you do decide to go nuts you could build a 10 second GTI-R pretty cheaply (compared to cosmo, or GTR etc). Plus they are fairly nice just to drive arond in.
MX5 will be much better on fuel, but looks a bit camp, and it's quite small inside so you may not be comfy in it. but it would be great fun on track and ok for just driving around.
SR20 S13 is a pretty chat car. they have horrible interior, most in your budget will be fairly shagged too, but they have SR20 turbo up front, 5spd in the middle and driving the rear wheels which is a recipe for fun. some downsides are crap brakes, 4 stud hubs and again, that nasty interior will make driving it every day pretty annoying, but it will probably be the best on track of the 3.