E.,
I've owned my share of dogs(and pets) and have volunteered at local animal shelters since I was 16. I also worked in a pet shop when I was in college and have family who breed German Shepherds.
In my opinion, I would stay away from terriers,small dogs,and aggressive dogs when you have children to consider. Yes, it is all about how you raise your dog, but sometimes, there are accidents and I know of too many children who have been hurt.
The pit bulls are a definite no no.
The best dog for children are golden retrievers and labrador retrievers. As a matter of fact, we are getting one for my children. If you buy from a breeder, be sure to visit the home so you can see that the puppies are well socialized from birth in the home and not in a cage.
The best type of dog that does not shed is the standard sized(not toy size!) poodle. They are the most intelligent dog breed. You may be interested in a labradoodle. They are a mix between a labrador and a poodle. They have the happy personality of a labrador with the intelligence and non shedding coat of a poodle. They come in medium to large sizes.
Supplies you can get at Petsmart.
Here are some reputable breeders in Dallas:
http://www.timshellfarm.com/goldendoodles.html
http://www.labradoodlebaby.com/
http://www.legacy-labs.com/home.htm
http://frogcreekranch.com/
http://www.texasgoldenretrieverbreeders.com/
Adopting is great and I am a big supporter but when you have children,you should get a puppy. The reason being, you will mold and raise your puppy to be kind and patient with your children. If you get an older dog, you have no idea how it may react to your children. Spending only 10 m inutes at a shelter with an older dog tells you nothing. My best friend has a scar on her chin from a dog who bit her. She adopted the dog from a shelter when she was 5 and it was as sweet as could be but a week later it bit her when she put her hand in its food bowl.
When you adopt a puppy, sometimes you have no idea what it is or how small or large it will grow to be. Since you state you want medium size and low shedding, your best bet is to go with a breeder. STAY AWAY from puppy mills and pet shops.
My son's(he is 2) best friend is our neighbors English Labrador Retriever. I have never seen a dog more patient. My son pokes him,rides him,pulls his ears and tail, and the dog is more than happy to let him do whatever. He adores my son. :) We just bought an English Golden Retriever puppy for him that will be ready to come home in about 5 more weeks. You should never get a puppy younger than 8 weeks old.
Retrievers do shed but we have hard wood floor downstairs and the dog will only be allowed in the downstairs areas with doggy door access to the backyard.