Two main things:
Allow you kids to pick out the dog they want. The animal shelters are full of canines who need loving forever homes, but it’s important your kids and the dog bond PRIOR to adopting the dog. That’s a spontaneous thing. When they encounter the “right” dog, they’ll know it, and probably won’t be interested in looking any further. This is important in ensuring the dog is loved.
Second, try to steer your kids toward a child-friendly breed. We had boxers when we were kids. They’re good around children, and they’re also very protective.
Observe how the dogs respond to the presence of your kids. Are they friendly and eager to be petted? Do they love to lick hands? Or, do they growl and bark menacingly? Are they stand-offish and reluctant to be touched? Kids need dogs that love being touched, because children will touch dogs many times and in many ways.
One other point: Be sure to teach your kids to be kind to animals, and that if they get a dog, they should be responsible for feeding it, keeping fresh water for it, and generally taking good care of it. You, of course, will have to take care of vet bills.
Some breeds of dogs like to dig. Dachunds (also known as Doxies, or wiener dogs) are diggers. So, if you have a garden you want kept intact, a Dachund might not be a good choice.
But again, if your kids bond with one, it may not be possible to pull them away.
The larger breeds need plenty of room to move around. A large yard is preferable, well fenced. Look into your town or county’s leash laws. There may be an ordinance against allowing dogs to run loose in your neighborhood.
Do you have a cat or are you planning to get one? Not all dogs get along well with cats, and not all cats will tolerate having a dog around. That, too, would be a consideration, if it applies here.
Good luck and kudos for wanting to adopt a dog and give it a good home. Please DO have it spayed or neutered.