A Civic EG hatchback is one of the best autocross platforms you can get. Numerous engine options, chassis and suspension upgrades and tons of aftermarket support.
Failing that, almost any compact or subcompact with a decent stock set-up will do nicely. Meaning your basic mid-90's Sentras, Mazda Proteges, Honda Civics (again), Mazda MX-6s, really old Accords, Integras, or even Ford Festivas or Focuses. If you want a rear-driver, the Miata is a good choice, as well (and it makes an excellent beginner, or even mid-level, track car, to boot...).
In autoX, it's not big power or RWD that gets you into the faster-half of the field. It's having a well-sorted, and preferably, light car with a good driver. Inertia counts for a lot when you're taking a zillion turns in less than one minute. Which is why you should start with a small car.
Whatever you buy, make sure you have the budget for brake pads and suspension mods. Tires can follow. It takes tires to make you competitive, but you can upgrade as you learn.
