I would have a look at the battersea dogs and cats home website, they have lots of good advice over what sort of dog would suit you. I think they have a little quiz thing which if you answer as honestly as you can you get a good indication of suitable breeds. If its not on there, try "our dogs" or just google, what is the right breed of dog for my family or something.
Is this your first dog? one word RESEARCH
Research what sort of breed you would like, if you would like a cross breed (only caviat with that is less likely to know dogs character unless its an older rescue dog), Once you have researched and decided on a breed, research local breeders, be very wary of people advertising in free ads etc. Approach your local vets and ask for recommendations of breeders etc. Be prepared to travel to get the right dog.
Then look at finances - big dog = big bills, from food to vets bills (big dogs need more aneasthetic and drugs according to weight and this makes a HUGE difference).
Labradors and retreivers are fab, traditional family dogs but don't be fooled, they are a working breed and need alot of exercise. If you do go for these make sure you get one from a pet line rather than a working line as their temprements likely to be very different..
Avoid mental dogs - staffies (which are generally brilliant with children, but just bouncing off the walls all the time) boxers, springer spaniels, border collies (really bad choice with children). Unless you have lots of time for training and exercise i would avoid hunting and retrieving dogs because they need ALOT of exercise and mental stimulation, they are working dogs.
How old are your children? will they be able to take part in the training? If so then a dog that needs training would be fun.
There are so many parameters.
Most dogs are good with children, when chosing a family pet it is more about considering the individual dog that the breed sometimes. I have had a rotweiller that grew up with my DD1, amazing family pet, other people would be OMG at that choice (NB, i have a LOT of dog experience and this is not a novice breed). Some peope swear by retrievers and labradors. Id avoid highly strung dogs like GSDs and border collies.
I think that just about leaves the bull mastiff then 