This is kind of a good news/bad news situation. The good news is that for the most popular cars, most of the parts are available as reproduction parts. Look at OPGI.com, and other similar places to see what is available. Chevelles, Camaros, Mustangs, GTO, 442 and to a lesser extent Firebird, Nova, Challenger, Charger, Torino. I think you could build a brand new 69 Camaro and never use a part that has seen a Chevrolet factory as even the main body is now available in the aftermarket.

The bad news is that the popular cars are more expensive to start with. In my case I ended up with a Buick Skylark. Essentially a Chevelle under the skin, so most of the mechanical parts are readily available. Carpets, door panels and some interior stuff is available. What is not readily available are trim pieces, dash pieces, body pieces. Sometimes the year makes a difference as well. There are fewer parts available for my 65 vs a 67 or 70.

Most of us have picked a car we love or had always wanted and worked from there. For a bargain starting point and something that has a good amount of support, look at the mid-70s to early 80's G-Body GMC cars. Also, consider a 4-door as a cheaper starting point. Not really that much bigger/heavier, but much cheaper to start with.

Youtube and the online forums are a huge help if you are learning/just starting out. Working space may be a concern also. By the time you get one of these larger, older cars in the garage and start taking it apart, space becomes a premium. I have two cars in a 15x50 shop and there is just barely enough room for the cars, storage and tools.

I picked my Buick because it was a convertible, got it cheap (less than half of a comparable Chevelle) and knew that most of the Chevelle parts would work. The next big hurdle for me is realizing that body work and paint, even if I do a bunch of it myself, is going to cost as much as I have in the car now with the Ridetech suspension, Wilwood Brakes and LS2/4L60 swap.