I don't mind a shelter dog either, but we want a puppy for sure as we have another dog and want to train from square one without established personalities getting in the way . If we can find a pup at a shelter , great.
If you have a breed in mind, it might be worth looking into people who breed show dogs...or any breeder that doesn't just breed them as a commodity.
I say that because with our dog, we were kind of in a similar spot as you in that we wanted a puppy to start fresh. Being our first dog, we weren't sure that we were good enough at this whole thing to possibly bring home some bad things we weren't equipped to handle (and I know, that's not the case with all shelter pets, we were just paranoid). We wanted a foxhound, and found a breeder who hunts them competitively. So he doesn't breed dogs with issues, since he doesn't just breed to sell, if he breeds issues, he has to deal with them. However, he is willing to sell from the litters he has, but it's not why he breeds. Now, with you looking for <15 lbs, obviously the hunting breeders are out, but if you can get ahold of some breed specific breeders who are breeding for a purpose (show), and not just as a commodity in themselves, I think you could up your chances of getting a dog from healthy stock.
Honestly, with the sheer number of unwanted animals out there...in general stay away from breeders whose sole interest is selling them. We throw away too many animals to just be breeding them to sell. But, if you find a breeder that does it for another reason (show/hunting, etc.), they may have a pup that's not perfect looking and thus not good for the show circuit, but otherwise perfectly healthy, and you're giving them a good home.
*edit: Or adrock's statement above.