I was raised on the farm where we raised cattle, pigs, and chickens. We hunted wild rabbits but did not raise any. Now as an adult I am limited on space and resources. So..
when running the numbers what livestock is the most economical to raise?
Cattle
Depending on the breed of cattle you raise Holsteins we butchered out at 18 months and Hereford or Angus we butchered out at 24 months. In most places they require at least 3 acres to raise livestock but if you only have 3 acres that is enough area to grow the alfalfa and grain to support this animal. To raise a steer to butchered weight requires 2 to 4lbs of grain and 3% of body weight per day in pasture or hay. Gestation is 9 months so you will have 1 calf per year.
Pigs
Dealing with pigs is a whole different thing. They usually reach butcher weight in 6 months and they need between 2 to 4lbs of grain per day but they will forage or root and they will eat a variety of things. They are also to me like a composting machine and can devour most anything. The down falls is the space along with when they get out they can make short work of a garden in no time. Their gestation is 114 days and usually have 8 to 12 (or more) per litter and usually have 2 litters per year. On the farm we put them in farrowing crates to have their babies because some sows will eat their young and they will also lay on them. My personal opinion is I really can't stand raising these animals.
Goats
I never had goats growing up on the farm but I had them as an adult on a previous farm. I cannot say enough good things about raising these as livestock. They are will eat about anything and even when my goats got out they never went anywhere except the front and back yard. I even had 2 does were the best babysitters for my son when he was playing in the yard. If he wandered where they felt he shouldn't be they would gently butt him into going back in the direction they wanted. You get both milk and meat just the same as cattle but with a fraction of space and grain a cow needs. Also the make up of goats milk is about as close as you can get to a humans mothers milk so in a survival situation this can mean life or death for an infant. From a good doe I would get about 3 quarts a day and I had 3 sons living at home so I would mix it 50/50 with instant milk. I fed my goats 1lb of grain and 1 leaf of hay per goat per day. A goats gestation period is around 150 days and they usually have 1 to 2 babies (kids) per birth. When raising for meat some will breed a doe back in about 30 days of giving birth.
Rabbits
I hunted wild rabbits (and still do) as a kid on the farm but I never really considered or ran the numbers on them as livestock in a survival situation until I listened to Nick Klein of the Hostile Hare during the Survival Summit. I had no idea that in a 20x20 space you can raise 3100lbs of meat! I knew rabbits reproduce at a high rate but I never really ran the numbers regarding space and feeding costs. A single doe can have up to 64 babies per year and that is alot of meat in a survival situation. Their gestation is 31 days and butcher weight is 5lbs or more and usually at 10 to 12 weeks of age.. According to Nick his choice of food is barley sprouts/fodder. Feeding alfalfa can produce kidney and reproduction problems so Timothy or Orchard grass is preferred.
Chickens
Most of us know about chickens that produce meat and eggs so I won't go in to this.
My personal opinion is the most economic as far as space and resources is a combination of goats for the dairy and meat, rabbits for meat, and chickens for eggs and meat.
Tell us about your experiences in raising the above livestock
Be prepared, not sorry