In my experience, no matter who the pet ostensibly belongs to, it's actually Mama's! You'll be the one taking the responsibility to make sure this living creature is healthy, happy, and socialized. Your daughter will be able to help just a little, at her age, but cannot take anything like significant responsibility. If your husband is like mine, he'll help a bit, but might not be as much into it. Remember that adopting a pet into your family is making a ten to twenty year commitment. (I'm not saying you don't know all this; this is just my standard lecture.)
A new pet is like a new baby in the family. Is someone at home during the day? If not, consider a cat or two. Cats do better at home alone than dogs do. Cats like attention, but they'll gladly be the boss of your home if you want them to. A dog, being a pack animal, *needs* a leader (that's you). If you're not at home to lead, he will attempt to be the leader, and you may not be happy with that.
Count on lots of training, attention, exercise times, and vet bills. If you are interested more in a dog, go online and check out the various breeds. Find out the distinctions of the breeds you're interested in. You could contact a rescue organization for the breeds you like; you'll find out about the positive and negative aspects of the breed from people who are really knowledgable about that type of dog. Consider mixed breed dogs, too, who sometimes can be the friendliest and sweetest you can ever find.
You may want to consider adopting an older (a few months old) pet instead of a baby, since you have a two-year-old. Our local humane society doesn't place young puppies or kittens in families with very young children. But there are shelter dogs and cats desperate for homes, through no fault of their own.
My children grew up with both dogs and cats - as well as fish, hamsters, and parakeets from time to time. Lots of fun!