Mature dog; mixed breed.
Many rescues have their dogs in foster homes for a long time and get a sense of the dog's personality. A rescue in Richmond trains every dog in basic obedience and some in agility. The dogs are trained by prisoners who use their skills to get jobs upon release. The coordinator is good at pairing the dogs with appropriate homes. My colleague and her 11-year-old son just adopted a great dog through them.
http://www.sos-penpals.org/
Partnership for Animal Welfare
http://www.paw-rescue.org is also good, but they don't have an obedience certification for every dog.
Mixed breed dogs are often healthier and heartier than the purebreds. They come in many shapes and sizes that are right for your home, kids, and activity level.
Far too many dogs and cats wind up euthanized in shelters every year; there are many great ones to choose from in rescues.
I'll also add that mature dogs are a better choice for families than puppies are. It's hard to housebreak an animal while caring for kids, and kids aren't the best influence on an animal learning the rules. One that is already trained and whose personality traits have manifested themselves is a safer bet.
I wouldn't trade my Shepherd/Rottweiler/?? rescue dog for anything. He is angelic with my daughter, tidy, well-mannered, and a perfect fit for our family. Watching him sit in her bedroom doorway, guarding her as she sleeps, melts my heart. He weighs more than she does (55 pounds to her 41) but wouldn't harm a hair on her head, nor let anyone else do so.
Assuming that the dog is well trained, don't count out dogs with Rottweiler in them. They are loyal, calm, steady, tolerant, and good with children. Can't say enough good about them. They like to have a job, and protecting a child is one that they do particularly well.
Terriers too, though they can be a little destructive if bored.
Have fun with your dog!