mohair is the least expensive--because its less like to cause an alergic reaction, and because its warmer than sheeps wool, for many years, mohair herders recieved a stippend from the (US) government, since mohair was considered a vital resourse.

the government planned to drop it (since they now see war in more tropical (i.e. mid east) to be more likely than wars in arctic areas (i.e a cold war with USSR 'turning hot) and the military need for lightweight, warm garment has decreased.(i remember reading about the fight, but i don't remember reading about the outcome!-so who knows, maybe it is still subsidized)

and yes, pet hair can be spun.

in the americas, there were very few domesticated animals (actually in the world there are very few!)

in S.america, the llama, alpaca and the vicuna, both were herded primarly for their fleese. but in N.America no sheep or other fleesed animals were domesticated.
tradition weavers such as the navaho, used cotton and wool from sheep that had been killed for their meat.

after the arrival of the spanish, the navaho kept old world domesticated sheep for weaving.

in the Pacific North West, a species of dog (a domesticated animal) was breed specifically for its soft white underbelly hair, that was combed (like angora rabbits are) and the fiber was spun into special ritual garments

N.American made fibers from plant material, (hemp, cotton, pineapple, bark) but primerally relied on skins for clothing.

wool (fiber from members of certain ruminates, specifically sheep and goats) is a special fiber. (different than Hair) its easier to spin, mostly water proof, but once you get it wet, it still retains most of insulating properties, its burn resistant, its naturaly stretchy, it easily felts and it takes dye easily--in someways, it is a miracle fiber!

other animal fibers, (llama/alpaca/vicuna, camel, rabbit, silk) each have some of these properties but lack many of them.