First off, what kind of dog are you talking about? That is very important in formulating your questions.
AKC registration is basically meaningless. I always joke that the AKC would register a ham sandwich if you sent them a check. People always emphasize that their dog or dogs sire/dam are "registered" or have "papers". Doesn't mean a thing. However... quality dogs should be registered too but in your case, I wouldn't put too much weight on papers.
Ask your breeder as many question as you want. If they balk or push back, find another breeder. Ask also if they are "code of ethics breeder". You are interviewing them and purchasing from them. They are not doing you a favor by selling you a dog. We know many breeders and the good, ethical ones will be willing to lose a sale if it means one of their dogs would be going to the wrong home. They don't mind answering a million questions because they believe in their breeding program and they want to learn about you too so in essence, it's mutually beneficial to ask questions. Our breeder asked us a ton of questions. We've since become good friends and have seen how she breeds and feels about her puppies. We have indeed seen her turn people away because a Rottweiler isn't right for them. Responsible and ethical breeders will want to know who they're dealing with as much as you want to know you're dealing with a good breeder. They invite questions, ask you questions, and are very open. You also want a breeder with some after-sales support like training or boarding. It's a sign that they're willing to establish a relationship with you and don't just want your money today.
Depending on breed, a good breeder should help you pick the right pup. In fact, they should be able to pick one for you based on your mutual interview and their observation and temperament testing of the pups. (Temperament testing is important as well as the breeder's ability to match the right pup with the right owner.) The sire/dam are important for things like hereditary disorders such as dysplasia and also for temperament so as much as you can learn about the sire/dam the better. You might not always get to meet the sire as artificial insemination is very common. Finding out the dam's breeding history is important too. Many unethical breeders over-breed their females and/or breed them too you/too old.
Sires/dams that are show winners are okay. It's a "plus" I'd say but still not a guarantee. We've been to countless AKC dog shows and we regularly see dogs that are horrible looking win. Also, being able perform in a show ring is pretty one dimensional. Talk about obedience and day to day tasks and it could be a different story. The AKC world is a strange one for sure. As I stated, it's a plus but not a deal breaker. The fact that there is a later litter with show winning sire/dam is less about the show record but more about whether that litter will produce a dog suited to you based on the sire/dam characteristic and temperament, AND timing. Timing is a big factor. You have to be ready and your household has to be ready. Don't let a breeder rush you because "this is THE litter you want to choose from".
Definitely get references. Do research about that breeder, even contact the breed club in your area to get referrals. There are MANY unscrupulous breeders out there so you much be very careful! It's a very competitive business and this is a living creature that will be part of your family for years to come.
Book recommendation: This book is a mainstay when it comes to new dog owners.
The Art of Raising a Puppy
Good luck and keep us posted. I'm in a bit of a rush so I probably left out some important information.