Over the past years I've tried all sorts of livestock before finally settling down with what I believe are the easiest ones for the small homestead farm. Chickens. Muscovy ducks. Sheep. Rabbits. Pigs.
Rejected from my personal choices are:
Cattle.....Difficult to contain when they have a mind to travel. Eat a lot of food. Big enough to hurt you easily. Laborious for home slaughter.
Goats.....Hard to keep fenced in with just routine fencing. Climb on everything. Destroy things.
Horses..... Require a lot more work to maintain. Eat a lot of food. Big enough to hurt you easily.
Turkey....Disease susceptible. Die readily from just about anything.
Ducks .... Noisy. Filth up a pond in a hurry.
Now, just because I've written them off my list doesn't mean that other homesteaders wouldn't be successful with them. And funny to say, just because they are on my "no" list doesn't mean that I don't have them! Yes, I confess. I own a horse and a goat. I own a horse simply because it gives me pleasure seeing her there and tending to her. Sure, the manure benefits the garden too. The goat is a daily reminder to enjoy life. Try new things. The goat is a challenge and it's hard keeping one step ahead of him, but he makes me laugh and reminds me not to take life too seriously.
Chickens are good suppliers of eggs and meat. Depending upon how I house them, I also get manure and pen litter for the compost. My little banties do bug control for me. Since I grow or gather much of their food, it costs me little to keep them.
The Muscovy ducks are easy to keep. No pond or swimming water required. Not noisy. Good producers for meat....plus some eggs. I allow them to produce ducklings. Selling the excess is never a problem for me. They self-browse much of their food from the pasture.
Sheep are easy to handle without injuring myself. I grass feed mine and use grain only as a training incentive, so my feed costs are low. Since I have hair breeds, I don't have to sheer them, a big plus. They are easy for the homesteader to home slaughter.
Rabbits are simple to house, feed, and slaughter. They are a good source of delicious meat. And for those so inclined, their pelts can be home tanned.
Pigs are for me the most challenging on my list, simply because they can be strong rooters and can be fairly weighty when time for slaughter. But I have taken advantage of that strong rooting instinct, using a pig to help root out unwanted trees and tree stumps. And although other homesteaders find a 200-250 lb pig ideal, I would opt for 100-125 lbs. The smaller size is easier to handle for me.
Fish. If one has the right set up available, raising tilapia or catfish might be a good option. I haven't tried it yet, but I am on the verge of plunging into tilapia raising. Since I haven't tried it yet, I don't know just how well they would work for the small homesteader.
Some of the more exotic livestock is a real risk, as far as basic homesteading goes, especially for beginners. Most are expensive. Most people don't know enough about them to keep them alive and healthy. Most local veterinarians know little about them. In this group I'd include emus, ostriches, rheas, llamas, alpacas, and other exotics. I don't know about you, but I bet I could kill all mine in the space of a month or two, just out of plain ignorance.
I chat with other homesteaders who have been successful with some really weird livestock. How about raising guinea pigs for pets and FOOD? I'm told that they eat a lot of food for a small amount of meat, but they produce really cute babies. Then there is Stan who raises iguanas for meat. And Bill who raises snakes for food. Well, to each heir own.