We rescued our last two dogs from the dog pound or dog shelter. Both have been very loving and adorable. They were both small dogs, slightly smaller than a beagle. Both of them had some terrier and or poodle in them and they didn't shed. They were both very active and loved my kids.
One of the nicest things about getting a full grown dog from a shelter is that the shelter house breaks them. Both the dogs we got knew to "go" ourside and it took just a few minutes to teach them to go in and out of the doggie door.
The second nice thing about getting a dog from a shelter is they have a play yard where you can take the dog and see how the dog reacts and plays with the family, especially the kids.
When the dog leaves the shelter it will have all its shots and can be spayed or nuetered. Sometimes the spaying/nuetering is your choice. Sometimes its mandatory.
The possible negative thing is that sometimes dogs get to the shelter because they were abused by their former owners. Both of our shelter dogs were abused by men, or at least I assume that's what happened by their reactions to me. Both dogs played wonderfully with the kids, but wouldn't go near me. I solved that problem with kindness and positive reinforcement. How did I overcome their fear of men, or at least me? I had a traveling job that took me away from home. I'd leave home most weeks Monday morning and return Friday afternoon. I'd call my wife Thursday night and tell her not to feed the dog until I got home Friday. When I got home on Friday, I'd take a hot dog and slice it up and fry it in a skillet. The fragrance of the cooking hotdogs would bring the dog to the kitchen. I would then put the hot dog slices in a bowl and let them cool off. I'd then toss the hot dog slices to the dog. (I couldn't get within 15 feet of either dog when I started.) Then I was the only one to feed the dog over the weekend. In about 6 weeks I had them eating out of my hand. Both dogs eventually became "dad's dog" in that when dad and the family called the dogs, they would both come to dad first.
When you get a dog from a shelter or pound, you save a dogs life. I've had AKC dogs and mutt's. I prefer mutts. When you get a mutt, the dumb dogs, the weak dogs (Bad hips, bad backs, mental problems), the mean disposition dogs are weeded out. They don't survive to breed with other dogs, therefore you have a better chance of getting the dog you really want.
BTW, the best kid dogs are either small or are herding breed dogs. I went to some sheep herding trials. One of the women showing off her sheep herding dogs said that her dog would "herd the kids" when they were toddlers and kept the toddlers from straying too far.
Good luck to you and yours.