My favorite meat bird is the Freedom Ranger. I've had healthy, active birds that dress out at about 4 lbs for pullets and 5 lbs for roosters aroun 9 - 10 weeks. My first year I kept one rooster and two pullets thinking to breed them for a second generation (they are also hybrids but I'd heard that second generation will be almost as productive as the first). I put them in with my laying hens and it went well for awhile, but the rooster was so huge and so insistant with the hens that he was injuring them. He went in the stockpot. The hens were fine through the winter, but they were such poor layers and such big eaters that I butchered them in the spring.
I also like the idea of a self sustaining flock, but if you are trying to feed something like a Freedom Ranger or Dixie Rainbows, you might find that they cost you more in feed than they save you in purchasing new meat chicks every spring. Also, I doubt either breed will hatch their own chicks, so you'll probably have to invest in an incubator.
There are multiple discussions about heritage "dual purpose" breeds on this forum which will breed naturally and produce a reasonable amount of eggs and a reasonably meatie carcass. However, from experience those DP roosters (tried those one year) take easiy 16 weeks to raise and even then are scrawny compared to a CX or Freedom Ranger. I keep careful track of my expenditures with every batch of chickens I raise for meat, and while those DP roosters were the cheapest to purchase, they were by far the most expensive per pound because of how long I had to feed them and how small they were at butchering time.
I suppose if I could forcast the end of civilization and had to choose one breed of chicken to keep my family alive I might pick something like a Dorking which are supposed to be very tasty, decent layers and good foragers as well as being good mothers.
