There are no hard and fast rules unfortunately. Your prime concern should be to find a dog whose temperament fits in with your family's needs, the time you can dedicate to the dog and the place you live. If you don't have a lot of time or space, a high energy dog that needs to run will chew up your house and ruin your lives because it is frustrated.
That said some of the larger breeds are very calm and docile. For example, a mild mannered Newfoundland or St Bernard are very good around children. Then again, if you have more than one child, and they like to play, and respect the dog (i.e. aren't always charging up to the dog, trying to grab it from behind, or hug it - all of which are dominant, threatening behaviors), then you may want to look for a more active dog. You can find this in the breeds above, or you can go with a more active Lab or Golden.
The best thing you can do is to do a little observing of what your children are like, jot down your likes and dislikes from what you expect from a pet, what your environment is like and how much you personally can give to the dog (because you will end up caring for it for the next 10 years or more). Then use sites like the AKC (American Kennel Club - akc.org)to research breeds you just like the look or sound of. If you have breeds in mind there is usually a club for that breed in every state which can direct you to more info or to reputable breeders.
When you come to get the dog, either go to reputable breeders and describe to them the temperament you are looking for, or go to a good shelter and make sure you get a briefing on what the dog is like. Once you have your dog, take it to obedience classes and train it. The dog will thank you and your life will be better for it. Dogs love to please us and training them educates both of you on how to work together to get more out of your lives.
Try not to rush into a purchase of a dog. Its going to live way longer than your car, and you wouldn’t just take the first car someone offered you. You never know, you may end up with something you never thought you would get, for example, a well bred, well brought up American Pit Bull is a very gentle and friendly dog. The nicest ones are lovable.