A breed that is bred to protect livestock would be ideal, their are breeds called the "flock guardians" that make perfect outdoor dogs, are friendly with children and all sorts of animals. The maremma sheepdog, Puli, Komonodor, Great Prynese and anatolian shepherd are all flock guardian dogs.
I would recommend a Collie as the best breed, although the long haired variety can be a handful to groom but there is also the short coated variety. They are very docile gentle animals, medium in size and even though they are bred to be with animals they don't have to nipping tendancys like other breeds which herd. They aren't very likely to wander either and have a real uncanny sense of direction, perfect for the large backyard. When you train one well you have the most perfect canine companion.
Generally if you have kids avoid small dog breeds, they tend to be more dominant. Avoid the hound because they have a high prey drive and often difficult to get along with other animals, same with terriers, and you''re obviously not a fan of guard dogs so don't look into those. Herding breeds are good but usually higher energy so you need to be willing to work them - a lot, as well as do a lot of obedience training. Mutts are great, you just need to pick out the right one to suit your situation.
Of course if well trained any dog, breed, age or history unconsidered, can be taught to do well with other animals.
Take in mind that every individual dog is different and not all labs are friendly or all rottweilers aggressive, the puppy you pick and the way you train and raise it will determine a lot of how the dog behaves. In your case try and choose the more laid back puppy in the litter, not the ones that jump up and flop all over you, but also avoid the timid, afraid and shy puppies. You want a 'middle of the road' and 'medium energy' dog because they're much easier to deal with and more kid friendly. If you want a dog to be good with animals and children alike then raise it as a puppy and invest in a lot of time supervising interactions to raise them well together.
Overall I'd go with the Collier, they are great docile dogs and sounds just your type.
