At the risk of giving a not very practical answer, here's my opinion: the bielefelder.
The bielefelder is a dual purpose chicken created courtesy of German engineering in about 1970. The roosters are huge. The hens lay about 230 jumbo eggs per year. The breed is auto-sexing so that on the day they hatch the chicks' gender can be identified. I think if a homesteader wanted a sustainable flock and could pick only one breed, the bielefelder sits at the top of the heap in terms of pure utility.
If you are looking for a very heavy dual purpose breed that have consistent egg-laying and hardiness traits, go broody enough to reproduce but not to slow down real egg production, longevity of laying years....then White Rocks are your breed. The roos get big and meaty, the hens are the heaviest hens I've ever owned and they consistently won out over most of the other breeds in my flocks every year at cull times. Of all my original breeds, the White Rocks were still making the grade at 5 years of age, with the New Hampshires and Black Aussies coming in for a close second. They were a little lighter in build than the WRs, but not by much. The White Rocks were my biggest gals.
I have all females...I can't really have any males because I live in the city unless I can slaughter them before they begin to crow.
If you can't have any mature males at all....you won't be able to have a sustainable flock at all, let alone one that you can eat.
What I meant to say is that I don't have a sustainable flock right now because I live in city but we are planning on moving out of the city limits at some point and would be looking for a good sustainable flock
It depends on your weather/region, your flock management style, your intentions and the breeds you choose whether you will have a self-sustainable flock or not. You want hardy breeds that are thrifty on feed, naturally healthy/hardy, good and consistent egg laying, broody enough to reproduce but not so broody that they slow egg production for long, good mothering instincts, good foraging abilities if you choose to free range~and this is about essential if you are looking towards self-sustainability, good survival instincts and longevity of laying.
If you free range you will want birds that are not too docile or complacent. If you want to keep costs down you need birds who do not eat too much, get fat as a result and slow down on egg laying or have reproductive problems because of the excess fat(one breed comes to mind consistently on this point~Buff Orpingtons...not ideal for self-sustaining flocks). If you have cold weather, you will want cold hardy breeds.
It all comes down to a variety of breeds that fit that description and then individuals of those breeds that are the ideal of their breed....this level of self-sustainability genetics in a flock may take you years to develope but will be well worth the effort in the long run.
Some of my favorite breeds for pure self-sustainability are the White Rocks, Black Austrolorps, New Hampshire Reds, Rhode Island Reds, White or Brown Leghorns, Partridge Rocks, Brahmas, and Barred Rocks.
One I've considered, after looking at the Hubbard site, would be a naked neck. I used to have some naked neck. They are big, gentle chickens, very hardy, less feathers to pluck, lay lots of big, brown eggs and seem to grow fast. Hubbard appears to be crossing them on a bunch of different maternal lines.
A friend of mine got the Slow White Broilers from Welp. I will never try to create my own dual-purpose cross again! Those birds are wonderful meat birds that will finish out before any of the traditional dual purpose breeds, but slower than the Frankenchickens. AND, the hens lay pretty much daily, even through the winter, no health problems associated with weight. They are active foragers and pretty even tempered, non-flighty birds. Their offspring have been as satisfying as the first generation though perhaps a little less consistent.
I'm a fan. Perhaps their only downfall for a homestead meat bird is their white color, which could potentially make them more vulnerable to predation if free-ranged.