I've bought a lot of my sheep at livestock auctions, both commercial ones for the farm and my fleece sheep.
I've also brought direct from the breeder in both cases.
Tups from breeders I know for my sheep; ditto and from the pedigree sales for commercial ones. Oh, and from recommendations in the early days too.
I've never bought through Facebook or FreeAds. I bought a lovely pony advertised in the local paper but in general wouldn't buy that way.
Cattle, I bought one Jersey after hunting down a descendant of a particular herd, then bred my own using AI.
On the farm, ex-BH bought cattle almost exclusively at livestock auctions, but predominantly from known breeders.
Until I needed working collies, all my dogs were rescues. I bought a part-trained 2-year old collie when I started sheep farming, from a respected breeder, trainer and triallist, and was given another experienced 2-year old dog by a local farmer, surplus to his requirements but a godsend to us. Dot was a present, accidentally bred but from excellent stock, and is the only dog I've ever had from a pup.
Cats rescues initially but now I seek out Siamese crosses - and have bought kittens found through newspaper ads.
Oh, and I bought some chickens found through a newspaper ad, too. I would probably happily source chickens through DASH ads (on FB) but wherever, I would always visit first to be sure of health status - decades ago, I had some disasters buying in chickens which weren't 100% healthy.
Blokes seem to land when I'm not looking. Trying to be more vigilant these days