With that kind of budget you're going to be looking at the 2nd generation cars which were sold from '90-'93.
Autocrossing is a venue which focuses more on tires, suspension and braking than engine mods. You get placed in classes with similarly powered cars with similar handling abilities and unless you go into a class which allows very heavy modifications you're kind of limited in the amount of mods you can do to the engine.
What's your total budget for the project, including paying for insurance, gas, maintenance (the car is going to be old) and all that other stuff?