Personally I think it's worth going along to a rescue and having a frank chat with them about your wants and needs. If they're conscientious, they'll only regime a dog with you that is proven good with children (and small furries) and has met every member of the family more than once. If they're just happy to give you any dog, get the hell out of there. The good thing with most rescues like dogs trust is that they provide after care too.
If after you've spoken to the local dog shelters and you feel it's not right, then do look at a pup but do remember that puppies are bloody hard work, messy, nippy and destructive. Yes, it's a more mouldable and trainable mind, but it really is like having a furry toddler and they take time to train.
Also, if you are going for a pup, please, please, please be responsible. Do research into breed types, then Save up and buy from a reputable breeder who has good reviews - don't go for a cheap pup on gumtree or the internet as they're likely to be puppy farmed, which in turn can lead to serious health and behavioural issues later on.
I've got two rescue dogs, from dogs trust, and our stipulations were that they be good with dogs and kids.
We met and walked our dogs on several occasions before we took them home (individually, 4 years apart). We had teething problems with both while we were getting to know each other, but with time, giving them space and building love and trust they truly are the best. They're loving and calm and it's really rewarding seeing how far they've come in their confidence and their training. Rescue dogs really are rewarding, but you really do need to take time, not rush and make sure the dog is right for you, and you for it before you even consider taking it home.