As others have said, training is key. Every dog is an individual and may not have a temperament typical of it's breed either. I would, however, take a breed's "purpose" into consideration when looking at dogs. Sighthounds (greyhound, whippet, saluki, etc) would probably be a poor choice as they have the desire to chase anything that moves, especially small "fluffy" things.) Same goes for most terrier breeds.
We have several dogs. I have Chinese Cresteds who I do NOT let around the chickens. They'd snap up a little chick in an instant but then get beat up by an adult chicken. They're tiny, but they don't seem to realize that. They think they can take on the horse too, LOL. My husband's dog is a Catahoula Leopard Dog, a breed bred and developed to hunt/herd feral hogs and cattle and pretty much any other critter you need either chased up a tree or subdued by baying and biting. Our houla has killed raccoons, rabbits, and once a coyote. What amazes me about him is that with almost no training when we first got him at 8 months old (free to good home ad, poor guy, better off now) he naturally took to our livestock. He shows little to no interest in the chickens, turkeys, or goats. He's a little afraid of the horse and donkey. The only thing he seems to get keyed up over is our rabbits, but he's learning to stay away from the hutches. That being said, I would NEVER trust him to be left alone with any of the other animals. He's a decently sized, powerful and headstrong dog and I never want him to be put into a situation where his instincts take over and he hurts or kills one of our animals.