Dan, Maybe that was your experience or impression, but lots of options for vehicles without a racing past. Yes there are a few organizations specifically for vintage race cars. For anyone starting from scratch, key is to develop within the rules targetted and you'll be fine.

For example, see Dave's post in this thread about
building a 1966 Trans/Am car where he updates the info I had posted.
Dave's Zebra Dart does not have a racing history.
Ritz's Team Starfish does not have a racing history.
Ott/Hagstrom 'cuda does not have a road racing history AFAIK.
The Benson's Dart and Barracuda do not have a racing history. They do run in an SCCA Open Class mostly because they prefer running radial tires. Remember you got to be having fun, or why do it.

There are other forms of high speed competition as well. Beckman runs vintage (european) rallies with his Ralleycuda (it does not have a racing history). These are sanctioned by FIA. Jess Neal's 'cuda has most fame for taking the vintage class 1st place at Pike's Peak the year Hot Rod magazine went along for the ride. Hill climbs are often sanctioned by smaller clubs in combination with bigger organizations. So the rules and classes at say Pikes Pike are different than say at Durayea or Giant's Dispair.

In addition to what Mitch and Steve wrote about going to events and clubs, look for websites and pages rather than vids. This is where you're more likely to find specifics about clubs, rules and people to contact.

If at the end it all looks too pricey, good places to begine are to find or start a 24 hours of Lemons team on one hand, or go autocrossing for a while with an old mopar. Several people have done both as ways of developing their cars, their driving, and their wheel to wheel skills.