Trans-Am info for the 1966 Barracuda
A lot will depend on exactly which sanctioning organization(s) you will be running with. Vintage racing in North America is done under at least a half dozen different groups each with their own rules. The FIA homogolation papers are a starting point for many but not all of the groups. AFAIK all require additional (anachronistic) safety items.
You may want/need a clean body with all the trim. OTH you may do just as well with a something a little rougher so you won't feel bad when you stretch the fenders. Depends on the group and the class you will be running with.
Currently running in vintage racing is Mike Ritz's Team Starfish car (not an original survivor btw) and Mapes's Zebra Dart (East Coast). There are a few others that run in more open classes. You may have seen the Benson's in Sportscar last year - they are running a '66 Dart and Barracuda. Closer to you there is second generation Barracuda that's made a few mid west council events.
Historically, for the first generation a-bodies, look at the Monte Carlo entries, and in the US/Canada at the Shell 4000, as well as the Trans Am efforts by Group-44, Brock Yates, and the factory teams already mentioned.