A dog can be a great family member, but not so great a Christmas present. Think of it as a baby (or young child) coming into your home to stay. The joy, noise, and confusion of Christmas can make the adjustment much more difficult than a quieter period of time would do.
If it were me, and I had definitely decided we needed a dog, I might give the family a dog leash and bowl for Christmas as a "teaser," and announce that some time after Christmas, when the right dog is found, the family will adopt it. That gives you time to do lots of homework.
My husband and I have raised pups for Canine Companions for Independence, so we've had experience with Labs, Golden Retrievers, and mixtures of the two. Their temperaments are generally very good, but how they're raised and treated makes a difference. Just like children, temperament differs even among pups of the same litter.
Any dog, however sweet, who is teased, hurt (even in friendly play), or frightened by a child - or grown-up - can become defensive and growl or snap out of fear. Some older dogs become stressed out by young children, probably also out of some sort of worry.
You can research different breeds - I believe there is an online organization for every dog breed (including mixed-breeds) on the planet! Pick people's brains. Talk not only animal shelters but to your local animal-adoption agencies. Many of the agencies do a lot of temperament testing, in order for the match to be a success. A friend of mine fosters for one of our local ones, and she interviews anybody who wants to adopt one of her foster pets. She's pretty demanding, too!
Outside of our CCI pups, most of our other dogs came to us, as it were - they'd show up in the yard and just stay. They were of varying ages and breeds, and most did just fine with our kids and their friends. The only major trouble we had was with a German Shepherd who decided to become too protective of the family. It was very sad because the kids loved him.
If you adopt a puppy, someone has to be responsible for training him, taking him out every hour until it's reliably house-trained, feeding him, supervising his play, socializing him, teaching him manners, etc., etc., etc. That work usually falls to Mama, even if it's the children's dog, because children just aren't responsible enough. (If a new little person came to your home, you'd let six-year-old brother help, but you wouldn't expect him to raise the baby.)
Hope this helps a bit. I hope you find your forever dog!