i like the AMC javelin myself but as magic said, some parts can be hard to find. for a cheap fix up the body type car that may be hard to find. i suggest looking at some used car dealers around where you live and if you find something that looks good test drive it a few times check the mechanics and such. try not to be horribly picky but dont overlook big mechanical problems. check everything before you buy. small stuff is easy to fix.
EDIT: as they said easyest way to make a race car is to get one mostly done for you, funnest is to make it yourself, though that can get pricy real fast
1972 AMC Javelin (someday)