Okay puppies/young adolescent dogs and young children from my experience.....
Puppies nip. Children do not like this and they howl. Puppy thinks child is playing. Puppy nips again. Child howls more. Puppy nips more. Parent's sanity is pushed to breaking point.
Puppies chew toys which are not put away. Young children are noitriously bad at putting away toys. Young child sees puppy with toy and snatches toy. Puppy thinks this is a great game of tug. Puppy has been rewarded for stealing and chewing toys and will forever more steal and chew toys. Children will howl when their favourite teddy/security blanky is ripped to shreds. Parent's sanity is pushed further towards breaking point.
Puppies need walking in the cold and the rain. Children do not like long walks in blizzard like conditions. Children whine and dawdle. Puppies do not like to dawdle. Puppy plays in the mud while child is dawdling. Parent now has one wet, miserable child to deal with and one muddy puppy to bath. Parent's sanity pushed even further towards breaking point.
Puppies love playing with and tormenting elderly cats. Elderly cats do not like this. Elderly cat moves in with the neighbour. The children gowl for their cat. Parents now at breaking point.
Puppy poos on the carpet. Child investigates with it's mouth. Parent has full blown breakdown and sits in a darkened room rocking slowly back and forth.
Again from vast experience:
Children and older rescue dogs - rescue dog has been tested with children and is past the nipping and chewing stage. Child and dog co-exist peacefully. Parents are happy.
Rescue dogs and cats: Rescue dog has been fully cat tested and is completely indifferent to the cat. Cat and dog co-exist happily.
Rescue greyhounds and walks in rain: You're having a laugh, yes? Walk in the rain? A geyhound? You've more chance of winning the lottery 
You sound like you have a perfect home for a dog, but not a puppy, not at this point, unless you place no value on your mental well being, in which case, go for it 