The broilers are bred to be eaten around 6 to 8 weeks of age. If the go much beyond that they are prone to have skeleton breakdowns or internal organ failure, usually the heart. You can keep them alive and use them in a breeding program by greatly restricting their feed, but that is a real balancing act. Most people that try fail. They just grow so fast the skeleton or internal organs just can’t keep up. Still, not everyone fails.
Many years ago, the first half of the last century, Delaware, New Hampshire, and some strains of the White Rock were used as meat birds. They could reach maybe 4 pounds at 10 weeks if fed properly and the bloodlines were good for meat production. When the Cornish Cross were developed, all that changed. People stopped breeding them for meat. If you don’t continuously select a chicken for certain traits, that trait can be lost pretty quickly. Those meat qualities were lost many decades ago for the Delaware, New Hampshire, and White Rock. There is not a lot of difference in any of those breeds and any other dual purpose breed from the hatcheries these days.
A few people, a very few people, are trying to breed the meat qualities of feed to meat conversion, rate or growth, and conformity back into those breeds. Some are developing their own flocks with those traits but with no regard to breed. If you can find someone actually breeding for that and can get some of their stock, even their rejects, you will be way ahead. Good luck on finding them and I hope you are willing to pay the prices they will probably ask.
With all that said, your plan isn’t all that bad. You may be disappointed in rate of growth and conformation of the breeds you get from the hatcheries, but that means you just start a little slower. I suggest you get a few different breeds of roosters and hens. Then eat the ones you don’t want to eat and breed the ones you do want to eat. The more different traits you are selecting for your breeders, the slower it will be, but you’ll be surprised at how much progress you make in just a few generations as long as you keep it fairly simple. If meat is your only goal, don’t worry about color or pattern, eye color, or things not important to your goals. Whether you include egg laying ability of whether a hen goes broody or not in your criteria is up to you.
In general, pick the roosters for meat qualities and the hens for egg laying qualities. They both contribute genetics for all traits, but a rooster doesn’t lay eggs so it’s hard to pick him for his egg laying qualities. You can see a size and conformation difference in hens and that may be part of your criteria for them. I eat my females as well as males but there are only two of us. I can get to meals out of even a decent sized pullet. Some people only want to eat males.
Good luck. It can be a good adventure.