If you want to limit your budget, the V-8 Mustang may not be the way to go. Though parts are relatively cheap and easy to find, a heavy, high HP car like that will (in all likelihood) be hard on the consumables like brake pads, tires, and fuel that make up the greatest part of your ongoing racing budget. Smaller cars like Miatas, or any of a myriad of Hondas are far more economical to run, and are every bit as much fun. In between you find the RX-7's, Datsun Z's, and BMW's that give you a few more ponies than the smaller cars, but still don't generally burn up the consumables as fast as a big V-8 car will.
Also if you are looking to get into this, it's far cheaper in the long run to buy a car that's already been built than to build yourself. It can often be several times more expensive to build than to buy the same car that someone else has already prepped.