None.
If you are expecting a kid to know how to self-defence after barely a few months or a year, other than that few fancy moves, he'll only get beaten to a pulp first.
If you are looking at an all round martial arts that would train their discipline, spirit and body - Aikido.
Just physical workout to burn him off - Taekwondo (there's a philosophy part that will come when he's going for his 2nd Dan or Poomsae), Karate, Brazilian Jujitsu, Judo, etc.
Physical workout martial arts these days have the "study" component relegated until when kids are older. Aikido incorporates these studies directly into the movement.