For brown egg layers, there's the Rhode island red, austrolorp, orpington, Plymouth rocks, and sex links. White egg layers there's the leghorns, anconas, polish, and javas. Pretty eggs, there's Ameraucanas, EEs, marans, and welsummers. For meat nothing beats the cornish cross, others ore the barred rocks, and marans .Obviously these are just a couple of popular breeds out of hundreds of breeds. Good luck!
Hi chicken dude I don't know where you live so cant say where you could get them form but, Australorps and RIR's are the most favourite, popular and known backyard utility birds since for ever. They would be your best bet. Jersey Giants(fantastic utility birds, but quite uncommon in some areas) Faverolles Plymouth Rocks Sussex (backyard meat production) Theses are some other breeds that are good utility birds.
All of your good egg layers will also make good dual purpose birds. These can be the Black Australorps, Rhode Island Reds, Barred Rocks, etc. Their meat won't be the huge drumsticks and wide breasts that you're used to seeing in the stores, but they are good homecooking! For the real "meat" chickens, you can get the hybrid meat birds from the hatcheries (Cornish X) and butcher them at 8 weeks old.