When you choose a mutt or a mixed breed from a shelter home, you are teaching your child the act of kindness. You are also, in a way, teaching them about the social responsibility that helps a good deal in the longer run.
As a general rule of thumb, always get the mid-size and the larger dogs. These are usually great for family and kids. Avoid smaller dogs, such as Chihuahuas, or anything that you can carry up with one hand.
Since adopting a rescue dog is a lifelong decision, it might be better to get a DIY dog DNA test kit to test for its exact breed composition.