What is the most efficient animal for wooded area in Midwest?

I was thinking about 1 pig a year or something like that but I'm not sure. I wanted meat first, then eggs maybe, wool would be nice.

Since you said meat is your #1 priority, I would have to say "Pigs". Notice that I made that plural. Pigs are very social animals, and fare better as a pair than as a solitary animal. Also, the competition for food causes them to eat more. If you raise a single pig to 150 pounds of net meat, if you had 2 of them, you would have probably 175# each.

Chickens are the #1 farm animal for several good reasons. They are easy to raise, require little input, and supply a constant source of protein year round. As winter approaches, you can cull the less productive ones and fill your freezer.

A simple formula for determining how many hens you need is:

Figure how many eggs you need per day, divide that number by 3, and multiply the result by 2.
Example: You want 12 eggs per day. 12/3=4, 4x2=8. You need 8 hens.

Of course, you may get more eggs in the warmer months, and fewer in the cold, darker months.

The above examples assume that you have ample forage for the animals. The more feed you need to buy, the less economical it gets. It is still worth it, even if it costs you more per pound than supermarket prices. You will be eating a flavorful, healthy product that the supermarket cannot provide.

Along the same lines, I would suggest seeing if you can keep a small number of each pigs and chickens. While I haven't yet been able to put this into practice, what I've read leads me to believe that being able to feed scraps from the pig harvest to the chickens and scraps from the chicken harvest to the pigs, as well as being able, if one has at least minimal paddocked space, to run each in the same space will lead to greater system efficiency. You can also throw whatever organic scraps you have into the sacrifice paddock and let the chickens run over them first, and have the pigs clean up whatever they leave. I know less about these than chicken or pigs, but goats might also be an option for you if you need your livestock to do something besides make meat, as long as you like goat milk and goat meat. Otherwise, if your concern is primarily meat, I would consider rabbits, if you like rabbit meat. Rabbits have one of the highest feed to meat conversion rates, so I've read.

-CK

Sheep actually are edge creatures from what I can see, similar to deer. Great for clearing out understory if you wish. They love vines too. Make sure they have minerals so they don't strip bark though.