I am 16 years old, I want to start training. But I can't choose between basketball and athletics. I like basketball, next year I'm going to change schools where I want to play basketball. But now I want to make sure that my body is ready for basketball stress and I want to increase my vertical so I think about athletics (I can train 2-3 months before moving to the other school). What do you think-should I start basketball and get experience or should I strenghten my body and then start basketball at the other school? (I've trained in athletics from 11-13 yo, but I've never trained in basketball)
P.S. I am 191 cm (6'4) tall

I'm not sure what school you'll go to or the competition level, but I'd say you better start working on your basketball skills asap!

Ideally I think you do both - train you're body and work on skills at the same time. There are plenty of dribbling, finishing, and shooting drills that will improve your conditioning. It won't matter if you can jump 40 inches or run a 4 minute mile you don't have ballhanding skills... the coach may never play you.

In my area, all the 6-4 kids that play for high school are skilled and have been playing a long time. Good luck and work hard at your dribbling, passing, catching, pivoting, lay ups, and shooting.