I have to disagree with squeaky about a rescue being "not worth the risk". Yes, you have to do your homework about any dog joining your family but just because they're a rescue doesn't mean they're any more of a risk. Young children also have to be "trained" on suitable behaviour around any dog.
Rescues, often smaller ones, have all or nearly all their dogs in foster homes, as they can't afford big, fancy kennels. Dogs in foster can be assessed, and are used to, normal family environments, often living with other dogs/cats/children/hamsters, everything! Therefore, you can get a good assessment of how that dog will fit into your own family.
Puppies are small, bitey things that poo and pee, need to be taken outside every 15mins when they're learning housetraining. They nip, get hyper around small, excitable children and are very hard work. It's up to you whether you want the hard work and commitment of training a small animal. Do you have the time/willingness to devote many hours to this?
An older dog, who has been in a foster home, is already used to smaller children might be a much better bet in your circumstances. Any fosterer worth his/her salt will be able to chat to you about whether they think that dog will suit you. Be prepared for a wait, sign up with several rescues, join their Facebook pages (usually more up to date than websites) and see what happens. If you plan to wait about 18 months then all the better. You've got time to get to know some rescues and to have a look at various breeds, although, to me, breed is less important than temperament.
Good luck 