There is a "right" breed for every family, and the best way to know if a particular breed will work for you is by talking to the people who are involved. I strongly recommend talking to one or more breeders (preferably at least one in your climate area) and asking specific questions, sharing information about your family & lifestyle, and meeting the dogs in person.
As a breeder, we appreciate when "puppy people" contact us well in advance of planning on bringing home a pooch (because honestly, we don't have litters of puppies laying around waiting for homes, we breed when we have homes waiting for puppies!). A responsible breeder will welcome your questions, invite you to their home to meet their dogs, point you in the direction of resources for more information, & be open/honest about their breeding program.
Doing your own research online is a great place to start, but truthfully, a lot of information can be misleading. For example, my breed (Rhodesian Ridgebacks) seems to have a rap for being counter surfers & needing a ton of exercise. In truth, I can leave my dinner on the sofa for a minute & return with it still there, & they tend to sleep 25 out of 24 hours a day, because they are hounds, not sporting dogs! What you find online will tend to be stereotypical behavior, & folklore that gets passed on from site to site as people copy information to post.
All this being said, the number one most important thing to consider is that no matter what breed of dog your family welcomes, you will need to do basic obedience & manners as a puppy (or even an adult in a new household), and there will need to be socialization & supervision with children. For ANY dog! Some breeds can be more problematic than others - herding dogs like shepherds can be mouthier, because of their original purpose. Toy dogs like Cavaliers will be less likely to bowl over a little child than a large dog, like a Doberman.
English bulldogs are a great breed for the right family. As Mamazita pointed out below, they do have a list of health issues... some more prevalent than others when careful breeding & pedigree analysis is not followed. So please, if you are considering getting a specific breed, do make sure to research your breeder & only get a puppy from someone who is responsible with health clearances, temperament awareness (not breeding ill-tempered dogs) & is a member of/follows the code of ethics of their breeds parent club.
You can get started with this link, for more information on the breed & a list of registered breeders:
I do not know any E.B. breeders personally, but if you have ANY questions about contacting a breeder, what to ask, what to be wary of, etc... I welcome you (& anyone) to send me a private message.
T. (Breeder/Owner Handler/Trainer Rhodesian Ridgebacks since 2000)