Smaller, skinnier chickens would do better in a forage-based arrangement than any larger, meat-type bird. "Game"-type birds would probably be the best bet if your main goal is to reduce or eliminate the need to supplement feed. The more you move toward larger, meatier birds, in general, the harder that's going to be. It's a continuum between wild, red jungle fowl-types, which can feed themselves just fine, and Cornish X on the other end, which can't at all, and there's no "right' or "wrong" place to fall on that continuum, but one has to recognize just how much distance and room there is between them!
The model that Ridgerunner is talking about that "has been used for thousands of years on small farms" didn't involve Cornish X, Freedom Rangers, or even, say, modern Rhode Island Red stock (their older ancestors, arguably). It involved scrappy little self-reliant landraces, more like the Icelandics, or what you see roaming villages and fields in "developing" countries--not hatchery stock or even most modern "heritage" breeds today.
They might look something like this picture of feral chickens: https://en.wikipedia.org/wiki/Feral_chicken#/media/File:Chickenfamily.jpg
Or this: https://icelandicchickens.wordpress.com/
Those types of poultry could work very well in the situation you envision. You don't get big, fat chickens, but you get quality meat with little input. However, for better or more likely worse, that doesn't jibe with most people's idea of a "meat chicken" these days. :)
And btw, I agree with the advice of locking them up at night in solid, predator-proof housing. Chickens aren't active at night, so nothing is lost by doing so, while many predators are. There is ample historical precedent for the value of locking up the free roaming chickens at night. You may still lose the occasional one to hawks etc, but that should take care of the worst of it.
Another thing to not to overlook in selecting free ranging breeds is camoflage! Note the muted colorations of wild jungle fowl--there's a reason nature didn't make them all white! :)
Good luck. It sounds like a cool and potentially rewarding project.