Yes, mice are good family pet. When and if the smallest children loose interest there is always an adult or an older sibling keeping the interest alive.
Children also need help with caring and feeding, so the whole family most be part of the ownership.
Mice love attention so I think it´s a good thing if the cage can be placed in a central place in the home - the livingroom for instance, or the kitchen (kitchen is a good choice in the beginning, so you can give it some extra snack when you are cooking food or having a meal and the mouse will learn that humans are nice).
They can throw some bedding out occasionally, when they get an urge to dig (and they live in a wire cage). Mice living in aquariums, terrariums or plastic cages obviously can't get much bedding outside of the cage. Inside the cage they are reasonably clean, mine at least tend to keep their peeing to a single corner.