I don't have any experience with beagles, but I am seconding the advice of picking the individual dog very well, once you've chosen your breed.
I have two German Shepherds that are as different as night and day, despite being from the same breed and looking very alike. My younger male shepherd is very protective and can be a big stress ball if he doesn't understand what is going on. He is a velcro dog, incredibly active, doesn't care for strangers, actively dislikes other dogs while on leash, and is not particularly good around small children because he doesn't understand the size difference issue (although he does LOVE children and that is part of the problem - he is just too eager for a 90 lb dog). My older female shepherd, on the other hand, is practically a Lab. She is a mellow ball of cuddles and joy, for everyone and everything. She will sit quietly with her tail wagging furiously as strangers come up to greet her. She is also tolerant to a fault - if she is upset with something that is being done to her, she will cry a bit, but would never snap or growl. Both dogs were rescue dogs and we were told right up front by the rescue that Jack (our male) would not be adopted to a house with small children. Sasha would have been adopted to a house with children, cats, small dogs, anything. A good rescue will know their dogs.
So, my advice would be to pick a breed (and maybe a beagle is the perfect breed for you - I have no idea) and then start looking into breed-specific rescues. With a puppy, it's difficult to know what the personality of the dog will be once it's grown up. If you look at slightly older dogs (6 months and up), it will be easier to get a dog that you know will work for your family because they will already be showing those personality traits. Only look at dogs that are living with foster families, not in shelters. Dogs in shelters seldom show their true personality, whereas dogs in foster families are often homed with children, cats, other dogs, etc. so you know what their strengths/weaknesses are.
My cousin and her family did extensive research before choosing their breed - a Nova Scotia Duck Tolling Retriever - and bought a puppy from a good breeder. They ended up with a nightmare - she's hyperactive, chews everything, barks and growls at strangers, cannot be around other dogs, and bites (including family members). This is not normal for the breed and they have had her in training since she was 12 weeks old (including hiring personal trainers/behaviorists to work with her) - it is just her personality. They keep asking me to bring my shepherds over to work with her on her dog-dog issues, but I just can't do it anymore. It was ok for Sasha to have a 8-week old puppy attached to her face, but now that the dog is over a year old and still hasn't learned any better, it's just not fair to my dogs.
So no matter what breed you choose, be careful with the individual dog that you bring home!