I'm assuming you're talking about IT racing as opposed to autoX or track day events...in which case I don't think there is an "el cheapo" way to race no matter what marque you choose. Unless you're leveraged to the hilt with deferred student loans or a TFB to fund your efforts, the actual car is a relatively nominal part of the equation, to wit: Schools, license fee, safety gear, tow vehicle, trailer, tools, race fuel, tires, entry fees, lodging, food ad, nauseum. Even the most budget conscious racers are gonna dump a minimum of $500 for a weekend of shits and giggles.
If I were a college student on a bufget and jonesin' to get into racing, I'd join SCCA or another sanctioning body and go to events and work corners, T&S, etc. Camp at the track. Eat the free food. Make a lot of friends and have a blast really cheap. Save the on track efforts until you can afford it.