As I stated in the other thread all dogs have health issues all breeds have issues. The only way to be certain you are getting a dog that will have few health issues is to go to a reputable breeder.
All dogs are different, even within a specific breed there are different personalities. Little dogs can be great dogs, it is a matter of training your dog and children to respect one another.
There is no perfect dog breed, they all have their pluses and minuses, for your requirements I would recommend getting a mature dog so you can be sure about their temperment... But here are a few that make good family dogs.
Boston Terriers- small, playful, some can have a lot of energy and because they are terriers may or may not like other dogs (get an adult).
Pugs- laid back, dont need much energy, are generally good with kids
Basenji- Great little dogs, are described as being more like a cat then a dog, can be high energy
Pit bull- can be high energy but are absolutely great with kids and people (were once called nanny dogs), they may or may not like other dogs
Mastiffs- big dogs but are laid back and need little exercise, they are great with their people but are aloof with strangers, most will warm up.
Poodle- Can be high energy and may need more exercise, great with families
Beagle- great with kids, a bit more low key then some other breeds
There are a ton of other breeds. I would recommend against herding dogs, some bully breeds and most terriers because of their high energy requirements. I would contact rescues in the area and let them know what you are looking for and be open about the breed, they know their dogs well if they are living in foster situations.