Before you make your decision, I suggest you look at the Henderson Chart for tendencies. Most production birds, which include most of the dual purpose breeds, have had a lot of the broodiness bred out of them. They were culled to leave only the best egg layers since eggs were hatched in incubators and broody hens are not laying hens. Some do occasionally go broody, but it is not a common occurence. And it is possible some people have developed lines that do go broody a lot, but you will certainly not find these out of hatchery stock. Hatcheries sell baby chicks and use incubators. To get baby chicks you need eggs. Broody hens do not lay while broody. Hatcheries are not going to cull in favor of broody hens.
http://www.ithaca.edu/staff/jhenderson/chooks/chooks.html
For your criteria, I would suggest you look at the Orpington or Sussex. At least that would be my top choices with your criteria if you are going with hatchery birds. Depending on your circumstances, the Brahma or Cochin could be a possibility. They are listed as broody and they will get large enough to eat, but they are slow to mature. The Brahma probably lays better than the Cochin.
If you can get your birds directly from a breeder who can assure you that they have been selected for going broody, any of the dual purpose breeds can be considered. Any of the Rocks (listed as Plymouth Rocks in the Henderson Chart), any of the Wyandottes, Australorp, Delaware, Dominique, Chantecler, Buckeye, Rhode Island Red or White, New Hampshire Red, and some I am sure I am forgetting. I do think your odds of getting a broody go down if you choose one of these production breeds. It is still possible as many people on this forum can assure you, just not likely.
Another possibility is to get two breeds. You could get one breed for dual purpose and one for going broody. If you did this, I'd suggest the Silkie or Old English Game in addition to the dual purpose breed. The Silkie probably bears confinement better, but if you free range them, the OEG might be a good choice.
Then you could always just get an incubator and raise them yourself.
Good luck, whatever you decide.
