Aaron, its very possible to do in my opinion. Just make sure most of the budget money goes for the saftey parts. Brakes steering and all that.
I bought my 49 plymouth for $100, So far with I have maybe $1200 into it and thats with having to buy a few tools I didn't have anymore after a few moves. Right now I got all the body work done. Only thing left to do it the brakes, steering and putting the engine and tranny in. And finding a rear window. My car would never be considered a show car. I would call it a daily driver. White trash daily driver LOL, Just kidding, All you need to do is shop around for the parts you are looking for. I got alot free from people wanting to get rid of them, Others I haggled the price down. As far as brakes go, I found a guy on Ebay I bought a Mustang MC from that is also willing to send me the front discs from a mustang for cost of shipping, 10" rotors, along with the calipers pads and all that.
So go for it, just find a cheap car to start with you can always finish it, sell it and get a better one.