Don't fall in love with a look. Fall in love with a temperament. Because that's what's really important. All puppies are cute and lots of breeds are gorgeous. But what you need is an animal that's gentle with children, patient and not a biter. I agree with the idea of getting a mutt, but one downside is that there's less you'll know in advance, so it does pay to know something about breeds, as every mutt is of course made up of two or more recognized breeds.
There are 7 groups of dog breeds as recognized by the AKC:
(1) Sporting - these are dogs bred for hunting. Pointers, setters, retrievers, griffons and spaniels are in this group. The labrador retriever and golden retriever are, as you have probably learned, the two most popular dog breeds in the US. The lab is #1 and by far, and both have been popular for a long time. There's a reason for this. They are good with people, good with kids and are very trainable. Labs and goldens make up a huge percentage of the service dogs in the US. Both will live for a thrown ball. The others are less popular although the cocker spaniel is still popular. The downside to a cocker is you will need to have it groomed, either professionally or you'll have to do it yourself (they have curly coats that will mat if they are not groomed regularly). They aren't as excited about a thrown ball but tend to be nice, too. Pointers are pretty large as are some setters (the Gordon, for example). Irish setters are well-known and tend to be kinda goofy. Irish setters and golden retrievers are also shedding machines.
(2) Working - these are the larger breeds and tend to be some protection dogs though not always. German shepherds are in this group, so are Mastiffs, St. Bernards and Newfoundlands. Oh, and Rottweilers, too, Malamutes and Huskies as well. Our Jake was mainly Mastiff and was a sweetheart, but he was also huge and a drool machine. I've had Rottweiler/Doberman mixes that have been kind of flighty. The thing with any of these is, because of their size, they are powerful and good training is a must. What's cute at the puppy stage is downright frightening later.
(3) Toy - these are the opposite of the working group. They are small (the largest is the Pug) and bred for companionship. Some are downsized versions of larger breeds, such as Toy Poodles, Manchester Terriers and the Cavalier King Charles Spaniel. Small dogs live a long time but are not necessarily without health issues. Cavs have an inherited heart issue which can kill them at a young age. Breeders are actively working to try to get that gene out of the population. Pugs can have breathing problems. Many of these breeds require grooming.
(4) Herding - Shepherds and Collies make up this group. Typical is the Border Collie; it lives for herding sheep and will herd your family if there are no sheep around. These are intelligent dogs that enjoy puzzles and will get bored if they don't have jobs. Bored dogs are destructive and whining. Some, such as the Old English Sheepdog are real shedders, too.
(5) Hound - these can be classified as either sight or scent hounds. Sight hounds are tall and often very fast runners. Greyhounds are in this group. Scent hounds tend to be short and squat, such as Beagles but the Bloodhound is also in this group. Scent hounds sometimes engage in a howling, keening cry that is loud and very annoying. We had a Beagle mix when I was growing up, and he barked at everything. A little barking is okay and pretty much all dogs do that, but this dog barked at falling leaves. Sight hounds are less barky but can be escape artists. You never, ever want to have one unleashed in the open as they will take off after a rabbit or whatever, including into the street, with no thought for consequences. Greyhounds go in bursts of energy but are otherwise couch potatoes.
(6) Terrier - these are small, prey-driven dogs. Sometimes they can be yappy. They are curious and can get into mischief. We owned a Staffie (Staffordshire, this is a type of Pit Bull) and she would quiver at the sight of a squirrel, salivating and ready to pounce. These dogs can also be diggers and some require grooming. Some Schnauzers are in this group.
(7) Nonsporting - these are the dogs that kind of don't fit into the other groups. This means the two bigger varieties of Poodle (Standard and Miniature), plus Boston Terriers, Dalmatians and pretty much all forms of Spitz dog except the Pomeranian, which is a toy breed. Temperament varies. Poodles need grooming. They are also water dogs, big time swimmers. Dalmatians can sometimes be deaf. Bostons can have breathing issues and snore like freight trains.
Keep in mind, of course, that temperament varies widely, but there is something to be said for what a dog was bred to do. And you can work that to your advantage in training, playing and having activities. Border Collies that love to run and corner are excellent at Agility, they can also be good at Flyball. Retrievers also like Flyball. Working dogs like Schutzhund and Skijoring. Terriers like Earth Dog Trials. Geryhounds like some Agility and Lure Coursing. Sporting breeds enjoy Hunting. Working breeds like Cart-pulling. ESPN sometimes shows dog sports and any and every breed can and will do any and every kind of activity, but you may find that a mainly sight hound dog is more interested in Lure Coursing than Schutzhund, for example.
One option is breed rescue. I believe that all recognized breeds have some sort of a rescue organization for dogs that have not worked out at their placements or were relinquished or found as strays or whatever. Try the AKC for this info:
http://www.akc.org/index.cfm Also, the AKC has a lot of other good information. Oh, and Greyhounds tend to have local rescue organizations that place the retirees from local tracks.
Very young puppies will require training and patience. Older puppies (about age 1) are teens and can be a real pain in the patoot. Older dogs tend to be past all of that, and then it's really down to temperament more than anything else. Some shelters do a better job training dogs than others do. I'd assume that any dog, even a trained one, would need some sort of training, simply to get the two of us used to one another, if nothing else.
Ever see The Dog Whisperer, Cesar Milan?
http://www.dogchannel.com/dog/experts/cesar/default.aspx?Google_Cesar Or Uncle Matty?
http://www.unclematty.com/training/allabout.htm Cesar tends to be more about the natural state of being of the dog, whereas Matty tends to be more about the inherent puppiness of dogs (domesticated dogs tend to be somewhat childlike so Matty plays off that). The methods differ and both have their followings.
Oh, anyway, I know this is long and I'm rambling, but to sum up, it's not going to be a perfect experience. For an experience with no whining, no poop, no walks and less shedding, get a cat.
) , so he will tend to keep an eye on toddlers - and back away if they start wobbling. 