A couple of chickens can fit in a cage (and do well, mind you) like a hutch that you would fit a rabbit in, and the modern breeds will produce approximately 800 eggs/bird over the bird's lifetime of about 11 years. More early, less later.
We have a meat goat (Boer/Kiko cross called a Texas cross or Genemaster) and three Pygmy goats. They take a yard about the size of a very small back yard, about 30 by 30. Most farm animals are hardy and don't require much space.
All my birds (meat ducks, laying ducks, geese, turkeys - OMG you cannot believe how good a heritage turkey tastes, Guinea fowl) all totaling about 40 birds, in a 25 by 25 pen with a small storage building serving as coop. They are healthy, happy and make the most fantastic eggs and delicious offspring for consumption. The real problem is usually city regulations. Most city dwellers can have hens, but you don't need a rooster anyway to have eggs. And many cities say you can have 5 , 12 or even 20 hens in your dwelling. Two hens will begin laying at around 21 weeks and will lay 1-2 eggs a day for their first year and then 1 every day or other day after that. They can live up to 15 years. And they're fun to watch.
As for butchering, I am close to a guy who will butcher a chicken for 2 bucks and a turkey for 3 and has a fast plucker. Means he gets the dirty part. I know how to do it, but it takes longer for me and is messier without the plucker.
As for butchering the goats, I have a neighbor a few miles away that has cattle (grassfed, lovely beef and makes his own amazing sausage) and so he will help me butcher when the time comes. Wafer (the meat goat) will be slaughtered at around 8-12 months and he will dress out at about 150 lbs, of course I will in actuality get more like 200 lbs or more, because I will also take the bones and lovely organs and just about anything I can from him, whereas many butchers only give you the meat, no or few organs.
Oh, in case you all think I am somewhere in SE MO or the outback or something, I live in the DC Metropolitan area, just outside the Beltway. Less than 20 miles from the "Big City". Washington National Airport's airplanes turn for final almost over my house. You don't have to have 100 acres and live in the boonies to raise your own food and it's often easier to do than keeping a cat or dog (I have three of them).
If any of you have any questions, PM me and I will gladly answer.
The eyes of all hope in thee, O Lord: and thou givest them meat in due season.
Freedom consists not in doing what we like, but in having the right to do what we ought.
Pope John Paul II