Canadian or Continental?
Canadian Kennel Club is pretty well equivalent to American Kennel Club for most intents and purposes.
A registration with Continental Kennel Club is basically pointless. They will register ANYTHING that basically looks like a purebred something or other based on PHOTOS of the dog. While AKC does not, as a previous poster incorrectly stated, guarantee a darned thing about the genetic quality of a dog, they DO track pedigree, and that's what papers are for. Frankly, that's all papers are for, when it comes down to it. If you are not registering with an organization that keeps *careful* track of multi-generation pedigree (and no, AKC is not the only one who can do this, just the biggest), then there is utterly no point in wasting your money except to fool your puppy buyers who think that just having "papers" means something nifty. I have a dog with blatantly *fraudulent* papers through ConKC and they said it wasn't their problem -- and per their charter, it isn't! AKC would have kicked the breeder to the curb for the same offense.
If you're going to breed show animals, you need to think about what organization you plan to show with. AKC is not the only game in town, but it is the most common, and I've learned that anyone who shows AKC-recognized breeds without having AKC papers is not always, but usually, a little sketchy. I'm not always a fan of AKC myself, but I do have to question why people would choose not to stick with AKC and their motives are rarely good. Now, if you're in a breed like Australian Shepherds, there can be breed-specific registries like ASCA, or Australian Shepherd Club of America, where you could do all of your show AND working dog titles through them without touching AKC. If you have a rare breed dog like Shiloh Shepherds or Cane Corsos, you would not be eligible for AKC and would want to look into venues like Rarities or ARBA or RBCSWO. But just as someone else said, if you're planning to be reputable, you need to have SOME measure that you are using to demonstrate, to yourself if no one else, what is the quality of your dogs. What are your main goals in breeding? Conformation? Working? What kind of work? Obedience? Agility? Herding? Flyball?
Yes, you're absolutely right that the dogs should speak for themselves, and yes, papers are just paper, however do make sure you understand what those pieces of paper represent. Not all papers represent the same thing.
One other note -- you can't lump all 150+ AKC breeds together under the same category of "too much linebred" or too much anything else. You need to look into the breed that you plan to become involved with, and you need to understand what is going on in that breed. Some breeds are much more heavily line bred than others. These are things you MUST understand before getting involved in breeding regardless of which registry you choose to align with.
My strongest advise is to go to some shows or working events, start to meet people involved in the types of things you want to get involved with, set up some appointments to sit and talk with some local breeders, and find yourself a really good mentor (or two!). Often, Yahoo! groups that are specific to your breed are a great way to learn from people from all over the country. It is utterly impossible to breed *correctly* without having good connections with other people in your breed, so you'll want to get out there and meet people.
Professional trainer, breed enthusiast, and performance competitor in several dog sports