I run a 1965 VW beetle in the HSCC Historic Touring Car Championship. Bought the car as a wreck, restored it, added all the safety bits, suspension and brake mods and tuned the engine...Total cost £15,000 (and that's with paying someone else to do all the work, so do it yourself for £12,000!)
Competitive?...Not yet cos i'm a newb to racing, but last weekend at Silverstone my 1300cc Beetle qualified 15th out of 21 cars with lap times quicker than some V8's and Porsches on the day and the bugs getting quicker every round.
Choose your car wisely and it can be very cheap.
http://www.youtube.com/watch?v=gP9NGNseacQ