I do not know if it is considered a sport but chess develops the mind. Many bachurim in Russia who played chess when they needed to relax from learning became gedolei Tora.
Regarding OP’s choices, football is a barbaric sport (the goal is to knock down people) as is NHL hockey (college and European hockey have a different atmosphere). Baseball is very strategic and is more brain than brawn. Basketball is not so good for someone who is not very tall.