Hey guy, the minimum age to join the military is 18, and 17 if you get permission from your parents. If I can, I will sign for you at 17 if I am still around, and you still want to join up. It might take both parents. If you go this early, you have to graduate high school first, and enter a program that pays for college when you get out for me to be on board.
I would be very proud of you if you joined the military, but you know how I feel about the different branches. I would REALLY prefer it if you got into a college ROTC program, or some other college program where you go to school, and then enter the service as an officer.
In this order from best to what I think is the worst. It is based on civilian careers afterward, and the least possibility of getting blown up or shot.
I think you should take steps to become an officer no matter which branch you join. the last thing you want to be is a grunt. There are not a lot of jobs waiting for a rifleman.
My first choice would be to join the Coast Guard. The Coast Guard academy is the hardest academy of them all to get into for a reason. But, when you get out, you will have a civilian career waiting for you. Any branch of the military will teach you a lot.
The Air Force academy also is pretty hard, but even if you become an ordinary airman, life on an Air Force base is pretty good. It is the most like civilian life of them all. It will also lead you go a good job after you get out.
Unfortunately, you are going to be too tall to be a pilot. Your eyes may not pass the test either, but that can be corrected. There should not be any restrictions for anything else. Do a lot of research, don't just sign up.
The Marines are really a branch of the Navy. You even to the the naval academy, and choose to be Marine officer at graduation. The marines don't have medics for instance. They are naval personnel.
My least favorite for you would be for you to become a private in the Army. There are the fewest career paths for a grunt. An Army officer would be just fine.
BUT, no matter what you do, I think the military is a good option for you. Be sure to get into a program that will pay for college. I have always hoped that you would go to The University of Washington in Seattle. I really think you would like it there.