Er, the obvious answer around here would be "chickens", of course <g>
But in fact I would say that that probably IS the best answer, chicken forum aside
They are cheap to obtain and cheap to keep; they are easy to take care of, aside from needing a bit more protection against predators than larger livestock do; they do Useful Things even if you do not get out an axe and eat them (i.e. they produce yummy eggs from happy non-battery hens); they will not trash large areas of land; and they are not a long-term commitment.
The only possible wrinkle with chickens would be that if you are in a cold-winter area (where are you?) you would need an actual coop for them to shelter in, but it could be a small shed-sized bldg up on blocks, it would certainly not have to be a Real Barn in any way. Some people spend lotsa money on their coop and run, but if you scavenge material using craigslist, freecycle, farm auctions, etcetera, you can do it pretty inexpensively yet well.
Or other poultry, although chickens are probably the best to start with.
Goats are real hard to fence in. Sheep and goats would need a barn type thing (not just an open shed) if you are in a cold snowy winter area. A cow would not do you a lot of good, might need a barn in cold snowy winter areas, is rather expensive, and is real likely to totally trash the land you keep it on. DO NOT get a horse unless you spend a year or so learning how to handle and take care of horses, realio trulio, plus setting things up safely for a horse would cost a whole bunch. A pig will TOTALLY TRASH wherever you keep it (concrete pen or pasture) and are hard to keep fenced in. Llamas and alpacas are Ex Pen Sive, and will need a good barn in cold winter areas.
So, all in all, even though this *is* backyard chickens, I would in fact suggest chickens
(Edited to add: I see from your other posts that you are in a REALLY cold winter area. In which case, chickens would be BY FAR the least expensive critter for you. If you are not convinced, btw, calculate the cost of fencing *alone* for all the non poultry animals you mention... fencing (effective fencing, that safely and reliably keeps animals IN and predators OUT) is really pretty expensive, and chickens you can keep in a smallish run.)
Pat
I've decided I'm gonna try to convince my father to maybe let me get some sort of critter.
