Dont bother about whether they are a KC accredited breeder or not, as some people registered on the scheme are puppy farmers. Try to find someone who comes recommended, what breed are you looking for, you would be better to go through one of the Breed Clubs and they would point you in the right direction?
Check up on what health tests are appropriate for the breed and ensure the parents have been tested, usually hip scored and in some breeds puppies are eye tested at around 6 - 8 weeks, but there are lots of different health tests dependant on the breed you are buying.
I would ask how old the mother is, and how many litters she has had in the past, I wouldnt touch someone who is consistently breeding each season off the same bitch and I would check what relation the sire is to the dam.