Autocrossing is (relatively) low speed racing. Most cars do not get out of second gear.
I've got a first gen RX-7 and it's a lot of fun on low speed stuff, even with 150k stock suspension. 2nd gens are less tossable than the fist gens and are slower than a good running first gen (especially a 13B 1st gen). You can pick up good first gens for $1000-2000.
But, I think the cheapest to buy and mantain would be Civic or CRX.
