I enjoyed Shoto-Kan at that age. It is a japanese karate that means "closed-fist." It does everything you ask of it and builds strength, as well as character. It is also a lot of fun.
Any martial art can be very useful at your age and position, they all have distinct advantages. For what you're looking to gain I would suggest styles like Tang Soo Do, Tae Kwon Do, or Shotokan, they all focus on those three factors quite a bit, I know I improved in them all after I started training!
However, much is to be gained from other styles as well, I suggest you look into what's available where you are and learn all you can, you might be surprised at what interests you!