You will need to do both on and off ice drills.
Your goal of becoming the best defenseman can be achieved but it isn't going to be a cakewalk. Getting to the Q at your age and scenario is pretty difficult, to be honest.
I would shoot to be the best defenseman or in the Top 2/3 first.
There are exercises you can do to increase core and strength on YouTube and specifically Hockey Training videos. You can buy training pucks and what not on Total Hockey and other websites to help off-ice stickhandling. I highly recommend the training pucks that force you to keep your head up as they are mostly white with a small black DOT in the center.
There are also "blindings" you can attach to your helmet to focus on stickhandling without looking at the puck, which defenseman need to be fluent at. You don't want to be looking down and have the puck stolen from you for a breakaway.
You should know how to skate backwards and do backwards cross-overs fluently so I highly recommend getting alot of ice time and possibly an instructor if you are serious about it. This could be done in the summer if you want. You can improve your leg strength by doing squats, running/jogging, and other activities.
There are other threads about nutrition and exercise on here if you scroll down the page a bit. They can give you better advice on the individual exercises and nutrition methods that are best for you. I use my own but it's kind of a bore and hard to explain haha.
Good luck!
