I think you'll find that when you go to a shelter, you won't find many cats of a specific, identifiable breed. I'm not sure where you are, but I know that locally, only about 25% of the pets surrendered are purebred and they get snapped up very quickly. Next to none come with papers proving they are pure. I wouldn't worry so much about the breed, especially if it is your first cat, as I would worry about finding a cat who bonds with you.

Go to the shelter, look at the pets, and ask the attendants what they know about the animals there. Are they friendly? Do they have a history of abuse? Medical problems? Allergies? Where they surrendered or found abandoned? If you are getting your first cat, you probably don't want one with a host of medical problems. It can be hard enough to take care of a pet without needing special diets and medication (that's not to say, however, that they are bad animals, just ones that need a lot of extra care and time).