If I were in a self sustaining mode of operation and restricted to just 2 types of animals I would likely choose Goats and Rabbits.
Goats can survive on the harshest of pastures or wood lots and thrive! That means there aint a lot of work involved keeping them for me as I am sure in such a situation I would already be plenty busy enough with other pressing issues. Not only can I get meat from a Goat I can also get milk, get butter and make cheese too. If you need to clear a section of a over grown lot, goats can do that for you in short order. Need the grass around the yard kept top a resonable hight, put a goat on a tether and stake them out and move them around as required. No problem.
Rabbits would be my second choice. Quiet, Prolific, minimal food consumption, easy to feed and take up very little space. You could grow a very small plot of alfalfa or Timothy Hay and feed them all year long on it. Conviently packaged in small dinner sized package allowing you to slaughter as needed and not have to do any preservation. Down side is little or no fat to them.
Now dont get me wrong, I do like some hogs for sure. Just a little more work to keep them up but pretty easy to do none the less. They reproduce well and are very robust and adaptable. Can be fed table scrapes if there are any and if not can be fed a wide variety of items and thrive on it. I also like chickens too. But they are a little too suseptable to pest and they would be pretty work intensive to feed in the winter especially if not free ranged. Free ranging chickens can make egg collecting difficult and you can loose a considerable amount of your flock to predators. Ducks could be a better option if you have a pond on your property unfortunately they generally dont lay a lot of eggs. But a few hens couild probably lay enough to keep you going and they are pretty tastey to boot when roasted or oven baked. I am lake front and the wild mallard population is quiet healthy hence the fact I chose rabbits over some type of fowl for the second choice.