If you think you can build a competative AI, CMC or AS car for under $20k you are in for a ride!
Of course, a lot depends on the region, but I thin you certainly can build a competitive CMC car for under 20k. The last two years the national CMC champion has been from the texas region, so I know these cars fairly well. I know of several cppetitive (in Texas,) CMC cars that were purchased for under $6000 (Adam Ginsberg's CMC car was a former AS car that he got for about $5k.)
There's a HUGE leap, cost-wise between CMC and AI. I figure a competitive AI car should cost around 12-20k, dependong on how fresh it is and how much was put into it (SLA front, fuel cell, etc...)
To build one, I'd budget $30k, minimum. A more realistic number would be more like $60k, I think.
American Sedan (AS)? You'd be lucky to build the motor for $20k! AS is a very old class, and therefore, very sophisticated. The restrictive ruleset means you end up paying a LOT of money for very small performance gains. This is how I see CMC ending up in 20 years, unless the series directors are VERY careful.
Stay away from the modular stuff... that engine is so much taller - raises the center of gravity, blah, blah If you can build the whole car yourself, welding, suspension set up, wiring, plumbing, etc. and can do it within the rules, you might have a chance at building something that will just do laps at the back of the field for $15k.
$15k is PLENTY to build a CMC car. I doubt Jeff Burch's national championship CMC car cost $15k to build.
$15k to build an AI car? Yep -- I think it's doable. I think it can even be a mid-packer or better, given the right driver.
But if you buy instead of build, you get triple the car for your money. Remember that. Building something and calling it your own has a lot of appeal (hell, I built my AI car from scratch,) but that appeal falls a little flat when you get your ass handed to you by cars in a SLOWER class!