First,
I do recommend checking out
www.petfinder.com It's a great adoption site for animals needing a home, and at least in my area all the shelters and breed rescues use it to list their adoptable animals. There are also some good education articles there about the various breeds. There's also a fairly good "breed selector" application at
http://animal.discovery.com/breedselector/dogselectorindex.do#apl_nav.
I do want to say something in defense of pure breeds. I've owned several pure breed dogs, and been around quite a few pure breeds as well as mixed breeds, and have never noticed a difference in issues with training or health problems. The main reason that there's a reputation for health issues in some pure breed lines is because they're known and can be attributed to a consistent breed as opposed to mixed breed dogs which may have the same chance of a problem, but there's no breed label to attach the problem to (I've owned two labs and a brittany and have yet to experience hip dysplasia). Admittedly there are some unethical breeders out there as well, particularly of toy dogs that are raised in puppy mills, but most AKC breeders are required to remove any dogs from their lines if they show signs of certain congenital problems. This is where I find AKC useful in that their breed documentation program tends to weed out the puppy mills.
In respect to training and behavior, in my experience a dog's disposition is about 80% nuture and 20% nature, and with a pure-breed dog that 20% nature is a lot more predictable and thus more manageable. If you have a good sense of the breeds mixed into a mixed breed dog you can obtain some of that predictability though. As for small dogs, I've found them to be just as trainable as big dogs. In general though, people tend to take the training less seriously with little ones because they can be physically controlled more easily. In particular I remember a chihuaua mix that was so badly behaved, if her mouth was larger she would have been put down by the city for viciousness, but because she was small, people would just shrug it off. Simply put, there's a lot more pressure to train a Rotweiller properly than a Bichon.
With all that said, there are plenty of dogs in shelters, and most of the breed societies operate rescue and referral services for dogs that are either of their breed or mixed with their breed so you don't need to go to a breeder if you want a pure-breed. This is how I adopted my Samoyed, and he's turned out great (although definitely not meeting the definition of a "low shed dog"). Rescues can come with their own complications though since often they've been neglected prior to the previous owner releasing them, but many times they'll be fostered by a local breeder and some of the initial work with them will already be done.
