Buying puppies is an absolute minefield, OP, so when you do decide the time is right (and I'd be inclined to agree your children are a bit young yet, but finding a well-bred pup is often a long process), then the first thing to do is decide on your breed.
I have no issue with crossbreeds in themselves, as long as they have appropriate health tests and are well reared - but the fact remains that the vast majority are puppy farmed and a fancy website talking about how well they do things is certainly no reflection of reality.
It is not so clear cut nowadays, but I would still say that the best advice is to treat licensed breeders with extreme caution. I know many dog breeders, and it is true that more true hobby breeders do need to be licensed now, depending on their local regulations, but when you are coming from it cold I'd still say that on balance a licence is an alarm bell rather than a comfort. This is even more the case with some breeds like West Highland Whites, Miniature Schnauzers, Miniature Dachshunds, Pugs etc. which are very commercial.
When the time is right, if you are unsure of the right dog, 'Discover Dogs' either at Crufts (at the NEC in March) or in London is well worth a visit. You can meet the dogs in the flesh and talk to owners about how they are to live with.
When you have decided on a breed, don't look for a puppy ... look for a breeder. It is normal to be questioned extensively by responsible breeders - good breeders have lots of interest in their puppies, they can pick and choose the right homes.
Only then, when you've found the right breeder, should you look to put your name on a waiting list and wait for a puppy.