we started with chickens, but I tell you, if I had it to do over again, I would go with rabbits first. They take up less space, no fighting, easy to take care of, and will provide a lot of meat in a short amount of time. They are easy to butcher, reproduce without effort, and are quiet and clean. Perfect starter meat. If you have a
yard, you have all the food a trio of rabbit needs.
I would start with rabbits, and then go with poultry. Muscovy ducks, guineas or chickens. If you want eggs, go for the Muscovies or chickens. If you want completely hands off, barely any feed requirements, go with muscovies and/or guineas. If you let the poultry get into the rabbit manure, then they will keep the flies under control and almost feed themselves (depending on the number of poultry vs rabbits).
Pigeons are another option, but we do rain catchment for our water, so that is out. No shit on the roof, please.
Goats are fairly easy, but they require good fencing, so if you are a beginner, go straight to electric
fence.
Dairy animals require a daily commitment, 24/7/365, so I don't recommend them to someone just starting out.
Pigs are easy, IMO. Give them plenty of room (electric
fence), fresh water in a nipple, and some shade. They do fine pretty much on their own (feral hog population in the US is proof of that). If you are a beginner, go with a smaller breed for your first few times until you get used to butchering and everything. Buy females (guilts), not boars, so you can avoid the whole castration thing. 2 feeder guilts will keep your family in pork all year. And a family of 4 makes enough kitchen scraps to almost feed one feeder pig. So, your feed costs can be quite low. If you are close to a dairy or a bakery or a distillery, get your pig food from them, and you won't have to buy much in terms of pig feed.
Bees are great, pretty much hands off, and don't require much in terms of feed. But, they do require a good location, so you need to keep that in mind. I don't really count them as an animal, they are more of cornerstone to any homestead. If you grow anything that produces flowers, bees are the logical compliment.
So, for me, it goes rabbits, poultry, pigs, in that order (bees being optional). Once you get a few years of animal care under your belt (and butchering, birthing, etc), then go towards dairy animals.