The various breeds of dogs were bred for certain specialties. Guarding, herding, killing vermin, bird hunting, retrieving, and so forth. So most purebred dogs have certain strong physical characteristics and instincts. Over the years certain breeds have become very popular, mostly because of their looks (Golden Retrievers come to mind). As a result they have been intensively bred, re-bred, and inbred, and all kinds of health and behavioral problems are showing up. This is why a lot of people prefer a mixed breed dog over a pure breed. They tend to not have extreme behavioral or physical problems. So, unless you really need certain predictable characteristics then you may be better off just looking for a couple of good mutts. There are some physical and behavioral characteristics that I look for in a homestead dog.
1. Not too big. Big dogs eat more, crap more, and are harder to take places. Not too small. If it's too small it will be prey for coyotes and other predators. A 30-50 lb dog is about right.
2. Not too shaggy. Some dogs' fur is like velcro and will pick up every sticker and burr, and become impacted with mud. A long haired dog will suffer in the heat more. Too short of fur means the dog may suffer cold weather more and be bothered by flies and mosquitoes more.
3. Some dogs are bred to wander and follow their noses. This describes hounds and hunting dogs. They are notorious for wandering the country side and causing trouble. I like a dog that will stay home.
4. Some breeds have a reputation for being unpredictable and dangerous (Pit Bulls, Rotweillers, Dobermans, etc). If you can't (or won't) protect yourself, and want a dog to protect you, then ok. But a dog like this may be a big legal risk. From what others have said, it seems that Large Guard Dogs have some of these issues, too.
For a general homestead dog, I like the herding breeds. The best dog I ever had was a German Shepherd crossed with Australian Cattle Dog (AKA blue or red heeler). I found him as an abandoned puppy. Heelers stay home, are sturdy, alert, very smart, and protective of their home, their critters, and their people. They have the perfect fur. Warm in the winter, but nothing sticks to them. But they can be suspicious and possibly aggressive to strangers. The German Shepherd in the mix made this dog bigger (65 lb) and more mellow with other people. And a coyote snooping around the chicken pen was his favorite plaything. My dog now is a blue heeler (rescued from the pound). People are always coming and going around here so she's learning to accept strangers pretty well. She patrols the place, and lays where she can see the driveway, the goat barn, etc. And she always barks and lets us know somebody, or something, is around. But, at 35 lb, she had better leave coyotes and javelinas alone. She knows that her job is watchdog, I'm the guard dog.