It can be done if you use your head and talk to people. Your not going to be able to have new OEM parts on the car your going to have "whatever I could find for $20" parts on the car. My first mr2 I brought for $300 and its a trooper its had a few engines but the first one lasted a few years, I rolled it, crashed it, spun it, slid it, 3 wheeled it, got it a couple metres off the ground and it still came over the finish line most of the time.
You might want to look into the early twin cam hondas as well (yes I am going to the darkside here
)those things can really haul and they don't break easy, you don't need a vteeeeeeeeeK!!!! just a fuel injected resonably good motor. We raced a DA1 integra at one point and we seriously could not kill that car it pulled 12k several times from noob gearchanges when we were using it as a lend a racecar. Honda or toyota are probably the way to go and if you can get a couple spare CV joints and things because if you break something like that it can ruin the "fun" (24 hours is a long time to constantly enjoy yourself)