I am going to do two takes at that at my own question. First, I am going to share what I would ideally do and then I am going to share what I would do if I had to do it tomorrow.
If, land, time, and resources were not an issue, I think this would be how I would go about it. I would want to be in a more secluded location with naturally occurring water sources, and plenty of pasture and terrain suitable for hunting and growing livestock.
Poultry & Eggs: I think I could easily raise a mixed flock of chickens and turkeys and be fairly self reliant. I think a mix of White Rocks, Rhode Island Reds, and Buff Orpington would easily provide all of your eggs and some meat to add to the pantry. Ideally, I would want a White Rock and Buff Orpington rooster to be the breeders. White Rocks and Buff Orpington add quite a bit of size to a flock. Buff Orpingtons are also reliable brooders and mothers. 25 hens and 2 roosters with 6 turkey hens and 2 toms would be sufficient in the poultry category. I have always wanted to raise Narragansett turkeys. I think between roosters, turkeys, and old laying hens you could can quite a bit of poultry from this flock. I would house them together in a fenced acre lot for the best protection from varmints and to keep them out of the yard. If you had a small pond, you could also easily raise geese for meat as well. If you had a small grassy area with your orchard and a small pond, two trios of geese would easily raise extra meat for the table. I would not house them with my chickens and turkeys though.
Dairy: I would prefer to raise a cow. The butter is the biggest draw for me compared to a goat. That's a great fat to use in cooking and I love butter. Cows also give a higher quantity of milk and you could make plenty of butter, buttermilk, sour cream, yogurt, ice cream, and cheese. Extra and old milk could be clabbered and fed to the chickens and hogs. You also would have an abundance to sell or trade too which could be an advantage. They also are not the escape artists that goats tend to be either. The calf could be sold or fed out to be a beef as well. I would be comfortable raising any of the main dairy breeds except Holsteins. They can temperamental and they do not have as high butterfat or protein content.
Beef & Pork: I do not think I would raise a beef every year or at all. I think I could make up with deer. I would want to kill 2 or 3 hogs a year. You could cure the hams, and bacon. I would can the sausage, and if possible freeze the chops. You'd have a great source of cooking fat with the lard you could render. If you could raise them in a wooded area with plenty of suitable foraging sites, you could minimize the grain needs. You could feed garden waste, and old milk as well. Hogs would definitely be the biggest consumer of feed. If you raised a few sows, you could sell the feeder pigs early and keep a few to kill later. That could help with feed costs. I think hogs would be essential for meat self reliance because you can preserve the meat a variety of ways and you can get plenty of lard.
Hunting & Fishing: If I could kill three or four deer in the fall, I would never want or need to raise a beef. That would be ideal. If you had reliably cold temperatures, you could keep the carcass store in a cold barn and cut what you needed from it. I would be more inclined to can the majority of it as ground meat and chunks. I think another overlooked piece to the puzzle is to take advantage of small game seasons. Kill your limit on squirrels, rabbits, turkeys, grouse, etc. to supplement the table. You probably won't preserve any, but it would be fresh meat in it's season which would be an advantage too. The same can be said with fishing as well. Catch and supplement as you go. If you can do it, freeze and can some fish as you go for later.
Feeding: I think you would have to develop productive pasture spaces for all of your livestock. Lush grass and legumes for the cattle during the spring, summer and fall. Grass and clover for the geese. Create an ideal environment for weeds, bugs, and worms to feed your chickens and turkeys. Be sure to provide any garden waste, milk, slaughter scraps, table scraps to the hogs and chickens. I think for your dairy cattle, you'd have to grow and cut alfalfa hay to keep the protein available in the winter. Raise or buy some grain to keep your cattle, sow, and chickens through the winter months. I am not an expert at all, but I think you always need to look for ways to interconnect your projects. Waste nothing.
Cooking: Ideally, I would have a gas cook stove in the main kitchen and a wooden range for the winter months. A good fire pit and a grill would also be handy in the summer to utilize for preparing meals and to assist in keeping the house cooler and conserving fuel.
Preservation: I would depend primarily on canning and curing. I would can all of the poultry, fish and venison. I would smoke, and cure the majority of the pork. We could go back to the old days and build a smokehouse. If freezing was an option, I would freeze the best steaks, chops, roasts, and a few whole birds and fish to eat. If refrigeration was not available, you would have to build a spring house or similar structure to keep milk, and butter chilled. Luckily, eggs will keep for a little while unwashed in a cool, dark area.
I agree with
@baymule it would be imperative to build a strong community of friends and family if this was a serious situation. A network of trading and bartering would go a long way.
Ultimately, no one can build a closed system of true self sufficiency. It is actually impossible. In this scenario, I have assumed that I already possess all of the infrastructure, tools, etc to begin with. I am also operating with the assumption that I could attain salt, canning lids//jars, and grain with little trouble.
When I get back from church, I will share what I would have to do right now if I was pressed to do so...