Not sure exactly who you want to share up to the next 15 years with? Start here to narrow your choices down based on size, activity level, temperament, coat type, etc.:

AKC breeds
UKC breeds
Even more breeds

Check out some dog shows to physically experience the breed(s) that intrigue you. Try to talk to owners/handlers; one who isn't busy will most likely be more than happy to discuss the ins and outs of the dog, i.e. grooming requirements, temperament traits, exercise requirements, etc. (A word to the wise: If you've never had a dog before, be prepared to talk, sometimes seemingly endlessly, dog. ) Check out the breed club's website to learn the possible health issues associated with the breed(s) you're leaning toward. Maybe join an online forum devoted to your desired breed. Personally, I belong to PitbullForum.com, and would be hard pressed to find a more knowledgeable, honest, caring lot of canine aficionados.
 
Now you know who will make your heart flutter? I advise going the rescue route when looking for a canine companion. You're saving a dog who ended up homeless, most likely through no fault of his own. (Some of the nicest dogs I have had the pleasure of knowing have been rescues.) A reputable rescue will help you choose the best dog for you and will offer further support with the breed. Give a good dog a home.

Have your heart set on a puppy? Puppies do end up in rescues, but you're still compelled to know from whom your puppy comes?

Okay, here's how I would choose a breeder:
Must get to know me, my plans and expectations for the dog, my knowledge about the breed, training, health and nutrition. The breeder should know more about dogs than I and want to talk extensively about his/her chosen breed. The breeder will remain in contact with me for the dog's entire life, and will offer help and support because he/she is a wealth of information.
Informs me of any health problems present in the line of dogs. Any breeder who tells me their line is 100% healthy is either lying or not keeping track well enough. Until we start cloning dogs, the crapshoot of genetics will produce an issue, no matter how slight.
Health tests for all conditions common in the breed; most breed club websites provide a list. Run from a breeder who thinks a simple once over from a vet is adequate.
If I ever need to rehome the dog, the breeder requires its return because she cares about and is responsible for every dog she produces.
Is only breeding to produce the best dogs because the breeder is always striving to improve dogs.