It is a minefield.
The KC puppy list is just an advertising medium that breeders can choose to use or not. In many ways, it is actually one of the worst ways to look at puppies without any further knowledge, as 'Assured Breeders' can add their litters free of charge (or certainly could, assume this is still the same).
Now, you would be forgiven for thinking that a Kennel Club Assured Breeder is a good thing, but unfortunately this is far from always being the case. In some breeds, this will mandate health tests, but in others there are no actual requirements bar paying a fee and being available for inspection (more of this later), so often you will find that it is high volume breeders on there.
Licensed breeders used to be an excellent red flag to avoid like the plague, but messing with legislation has meant that often the good hobby breeders also now need to come under this banner.
Unfortunately, there really is no fool-proof method of buying a puppy these days. Champdogs are perhaps one of the better ones, as they do actually insist on proof of health tests appropriate to the breed (but not always the ones they should, hence some breeds you will rarely/never see litters advertised on Champdogs).
I would start with the breed club, see which health tests they mandate and whether they have a puppy list. Various breeds will have central websites set up by enthusiasts - e.g. if you want a Rough or Smooth Collie by any weird chance, go look at Collielife.