As a future homesteader/dairywoman, the most interesting Pyrenees type dog will be a dog with a family and/or personal record for success with small livestock. I have a couple thousand dollars wrapped up in genetics I've been carefully shaping the last 10 years, and one hour of a visiting domestic dog could wipe most if not all of that out. Let alone a cougar (if you don't think they don't hunt for sport in addition to food, let me introduce you to Kenagy Katahdins...), bear, coyote and the increasing threat of wolves. Bobcats and eagles can also take kids and lambs. I anticipate being in the market for between 2 and 5 depending on my predator load. My first one, I will be interested in ability with stock, staying home, and repelling threats. The subsequent ones I will become more selective on breed and health (hips, etc). Likely an adult if possible for the first one and then pups after that (a good adult can be $1000 or so).
I will be looking for purebred LGD breeds or crosses between nothing but LGD. For a general farm dog, a non-LGD cross can be fine, but I don't play Russian roulette with a couple thousand dollars of hard work! Should I be able to add another goat breed I have my eyes on, and dairy cows, then the stakes raise yet higher.
Pyrs seem to have a reputation, at least in my area, for being wanderers and hard to contain. Some of them simply not showing back up because they wandered so far. I've heard varying reports of great and awful on Anatolians, Kangals and Akbash, generally good reports of Maremma, and then you get into the less common and downright rare breeds (which ethically should be bred pure - at least the females - in order to preserve the breed...I breed rare breed goats...crossbreeding pure rare breed females makes me cry inside). Some of the less common Turkish and Eastern European breeds have also been bred as fighting dogs, and if you aren't careful, you wind up with an unstable, useless dog. You also see the LGD/nonLGD crosses from time to time...again, they are great for general farm and family dogs...but you are better off with a full LGD for your stock.