Proper way to pick up a mouse is by picking it up by the root of the tail, not by the tail itself. Never carry a mouse around by the tail. Pick it up and put it on your palm. Even a mouse that runs away from your hand in the cage usually will sit very trustingly on your hand. If you are uncertain about your mouse's reaction, do hold it very gently by the root of the tail while the mouse is sitting on your hand.
Never squeeze a mouse, it is so lightly built it will get broken. No dot let young children handle mice. Children do not know their own strengths and can accidentally kill a mouse by squeezing. I wouldn't let a child under the age of six to handle a mouse myself, but I am pretty tight with mouse matters. Mice will bite in self defense if you hurt them. However, tame mice will not bite. When your mouse gets to know you, it will love to have you scratch gently behind its ears and being caresses by you. Mice are so small they don't play with you, but on you. However, mice are dun to interact with. You can teach a mouse its name and even teach it small tricks like standing up or climbing up a rope with treats. Mice love to run on you and around on the floor.
Before letting your mouse out of the cage, do make sure that the environment is safe for mice. The mouse must not get into hiding behind or under furniture or in cracks in the walls or floor. Go around the room with your eyes in the mouse level to see if there are any small cracks you don't usually notice from your eye level. Electric wires should be lifter up to prevent mice chewing them. What is very important - make sure that no-one steps on the poor mouse or kill it by trapping it with a closing door!!!!