With proper hunter safety, there is nothing wrong with a .22 rimfire. Make sure of your target and what lays behind the target. Be aware of what is going to stop you .22 round. Once you pull the trigger - nothing brings that round back. Be aware that a .22 round can carry over 1 mile.

Find a Hunter Safety Course and take it - would be a great Father / Son outing. Instructors make Hunter Safety fun and interact with students.