Can you add more about your experience with raising dogs and what your concerns are? All kids want a dog and they say they will take care of it, but that wears off by the 2nd day and then it's YOUR dog to fed, train, walk and clean up after!
Do you want/need a specially trained service animal? If not, what are the special considerations of your middle child? For example, do your kids rough house a lot? Then you don't want a small, fragile-boned dog. Does your 9 year old react to high pitched sounds? Then you don't want a small yappy dog. Do you have a fenced in yard? If not, then you don't want a big, active dog in need of a lot of exercise.
Are you prepared for the training and care of a puppy? Do you have experience with this and do you know how long it will take? If not, consider going to a shelter for an adult dog that already has some training and is housebroken. You still have to retrain them to your home, but at least they have a head start. Rescue dogs have special challenges, so figure out ahead of time what you are doing re access to the entire house or not, where you will confine or crate the dog, what you will do during the day (school and work), and what you will do on vacations (take it with you, board it, etc.). Are you going to let the dog on the furniture? Then you don't want a heavily-shedding dog like a golden retriever.
A lot of rescue dogs need special attention, which can be good for a kid who wants to cuddle all the time, but not good if you plan to leave it a lot (it's already been abandoned once, and may be sensitive to being alone during the day or kenneled during vacations.
The best thing about shelters is that they KNOW the dogs! They know general characteristics of certain breeds, but they also evaluate each individual dog for its own personality. A huge percentage of dogs at shelters are mixed breeds, which can give you the best of several worlds.
When we rescued our dog, we had a 5 page application in which we had to detail our knowledge, experience, our budget, our plans if we moved or traveled, the makeup of the household, and much much more. I'm so grateful to the shelter for doing this because they really gathered a lot of info and made a really good match between family and dog. She's a snuggly, cuddly lap dog and doesn't shed, but she would not have been a good match for a family of kids! Our neighbors got a larger dog, about a year old, who is terrific with kids - the point is, work with someone who knows the dogs as well as their pedigree, and consider a mutt as well as a thoroughbred. If you do not have a lot of experience with dogs, promise yourself now that you will go to dog training classes - they're more for the humans than for the dogs! Most "bad dogs" just don't have good or knowledgable owners.