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.