Call of duty finest hour ok for your 13 year old son to buy

Certainly. To be honest you should let him get Modern Warfare 2. My parents are extremely strict and I got my first ever war game when I was 13 which was Call of Duty World at War. I loved it and it didn't effect my daily life (increased aggression etc.) You should definitely let him get a war game but Finest Hour may be a bit old. Your kid will know (I am roughly same age) everything that happens in ar games anyway so you don't have to be worried.