Best dual purpose breed for sustainability

Nobody has mentioned naked necks (turkens) they are the most reliable layers, best at adapting to severe temperatures and easy to tame, they can be medium large but eat less than the really large birds like orpingtons, and when I lived in a city that didn't allow chickens, 6 of them gave me enough eggs for my husband and I to survive on while being fairly quiet. If I had to pick only 1 breed to survive on, it would be naked necks hands down.

Okay, so I put ducks on here earlier. Somehow I wound up with English Orpingtons along the way since then. YES on the dual purpose. Mine lay fairly well in the winter too. The cockerels also stay tender for a very long time so you can leave meat on the hoof. They're also calm, even the males tend to be non-aggressive, and they taste really, really good. The drawback is how long it takes them to mature, but at least mine tend to be fairly hardy and seem to not randomly die. Very broody and good mothers once they figure it out. They also forage pretty darn well for something that big. I'm won over. So for now I'm keeping Muscovy, English Orpingtons, and Khaki Campbells and we're flooded with eggs and meat and pest control.
...and of course we added dairy goats to our mix too, but that's another story.

Out of the breeds you mentioned, I'd go with black Wyandotte and buff orpington.
I love wyandottes, and have had quite a few broody ones.
Gamefowl and wyandottes qould be my pick. I'd put a Wyandotte rooster over a couple game hens (and Wyandotte hens...) and keep a cockerel from which ever game hen set eggs. He will carry the "broody gene" and pass it along to his daughters.

Good egg production and ability to brood are antagonistic traits to each other. Get some games and some leghorns, run the leghorns inside the coop and the games outside.

I know this is an old thread, but I figured it couldn't hurt to chime in for the benefit of newer members. I've had Australorps ("Australian Orpington") for 7 years now. They are hard to beat for a dual purpose breed. Mine produce a lot of large to extra large brown eggs and are still laying about 3 a week at 7 years. An Australorp hen holds the record for the most eggs laid in a year and they hold numerous records. They are very hardy, I'm amazed at the conditions my girls have survived over the past 7 years. They are excellent foragers and but tolerate confinement. There is some debate how reliably broody they can be, but given a large enough flock I expect you'll get a brooder out of the lot. You can add an Orpington as a brooder, but you'll get fewer eggs. They are a calm and quiet breed, and quickly adapt to human contact.

I just replenished my flock with another 10 Australorps and was able the throw the chicks in with the big girls with no problems. The alpha female took them under her wing and is quite protective.