I'm going to hop in here because I have experience from both sides of the fence.
1.
Adopting a pet from a shelter/Rescue Unit/Specific Breed Rescue: Truely a noble thing. The United States is very over populated with dogs and cats. You might not realize how badly. Just some facts from the Humane Society of America:
~Number of cats and dogs entering shelters each year:
8-10 million (HSUS estimate)
~In seven years, one female cat and her offspring can theoretically produce 420,000 cats.
~In six years, one female dog and her offspring can theoretically produce 67,000 dogs.
~Number of cats and dogs euthanized by shelters each year:
4-5 million (HSUS estimate)
http://www.hsus.org/index.html
A good way to help prevent this overpopulation problem is to spay and neuter your animals. It's NOT cruel, and has actually been proven to EXTEND the lives of cats and dogs. Shelter dogs/cats are good animals who need a LOT of love. I wouldn't expect to train them past the normal sit/stay stuff (it also depends on age). my two dogs are wonderful and loving and just great. Ok, off my little education soapbox.
LXA~Shelters are mostly full of mixed breed dogs and cats. Only about 25% of dogs in shelters are pure bred. A lot of people turn to pure breeds because mixed breeds can often be a 'surprise'. With a pure breed, you know what you're getting into. You can check out books in the library that will inform you of the habits and training methods best for each specific breed, but when you have a mixed breed dog--it is hard to estimate how to train your dog, how it's temperment will be, and what type of conditions the dog is best suited for--and these are major factors in raising dogs. If you have a dog that is mostly a beagle, for instance, you don't want to confine it to a small one bedroom apartment and expect it to be a lap dog. Beagles need excersize and places to run. The problem with mixed breeds, however, is it is often hard to determine which breeds might be in the dog. Some are easy, but some are very difficult/impossible. I have 3 animals (2 dogs and a cat) in my house, all from the shelter, all mixed breeds. I've had quite a few surprises here and there from my dogs and cat due to this. I still love my babies though
2.
Pure bred dogs from a CERTIFIED trainer: This is your best bet in finding a good dog. This is why lots of people buy from breeders, because they produce good dogs from good parents. They know what they are getting, they know how to prepare, and they have a dog that in the future can be trained for show. Showing dogs is a great 'hobby' or career and is fun. Lots of people enjoy it and enjoy furthuring a particular breed of dog and really can appreciate the features and abilities the dogs have. A good certified breeder doesn't care about the money they get for the puppy as much as they care what kind of HOME the puppy is going to. They want to see their puppies grow up respectfully and be a good example as to what their breed is about. They work hard to track dogs lines to produce great dogs.
3.
Breeders you typically find in the newspaper and Puppy Mills:
These are considered 'backyard' breeders and Mall shops get their dogs from Puppy Mills. NOT a good place to start. Get refrences. These people usually breed dogs in poor conditions to poor animals. You don't know WHAT you are getting. Puppy mills breed dogs too often, producing poor litters that will most likely be more likely to get infections and diseases and die young or as puppies. They churn out puppies for PROFIT.
My 2 dogs came from the shelter this time, but in the future I'd like to get a pure bred dog to train and show (I'd like a great dane). If you respect and admire a specific breed, I suggest finding a breeder and getting a puppy. But if you just like dogs and want a good companion, I'd go to the shelter first.
OH--another thought--shelters are starting new foster programs throughout the US. If you're looking for a dog, try fostering one first to get to know it, then maybe adopt it.