I've been racing in ChampCar (previously ChumpCar) since 2014. We currently run an E36 (similar to Spec 3, but the car is actually cheaper to put together.
The cheapest way to put a race car on the track and race is to buy a car already built. We bought our E36 (raced another vehicle before that that we built) as a finished - but older - race car and that was the way to go. I think we paid $7k for the car ready to race with quite a few spares.
And, in a plug for ChampCar, I think it is by far the best $$/lap value out there. You'll need at least a couple of teammates for the races as they range from 7 to 14 hours long, but we can do a whole race weekend easy for $3500 or so.
Our next race is Carolina Motorsports Park in June.
The beast about to pull out of pit lane at Road Atlanta last Feb:
