If you are looking to boarding school in the US, and if your child is athletically inclined, then you should do sports that are available in the US, such as soccer or swimmng. The reason is because your child might want to use the sport to get into a good school. Basketball might be a reach unless your child is tall (although you won't know now). Badminton is fine since your child can transfer the hand-eye coordination to other racket sports.