Marques, I would highly recommend beginning directly with a BS in Athletic Training. Currently, only a bachelor's degree is required to become licensed. (see https://www.nata.org/about/athletic-training/obtain-certification)
Then, as you practice in the field you'll see what areas interest you and choose a Master's program (if you want to continue school) based on your interests: options include Sports Management, Strength Conditioning and Performance, Biomechanics, or even a Master's in Athletic Training. Each of these will set you apart in different ways.
As far as getting increased experience while in college, unless your heart is set on working with Division 1 teams, I would recommend attending a smaller (usually less expensive) university. They tend to utilize their students more and if you come out of school with $40,000 less in debt, you'll be better off.
Also, I would ask your school's athletic trainer to volunteer now, don't wait until college. The exposure will help you during your undergraduate as you'll have real experience to use in order to understand vague concepts.
You can also visit the NATA website for your state (see: https://www.nata.org/about/districts-and-states) and look for nearby conference. Email the coordinator and ask if you can volunteer. They rarely say no, and you always get free admission for doing so -- if you do that once a year until you graduate you'll meet dozens of potential coworkers and mentors, as well as learn A TON.
I hope my essay wasn't too long. Best of luck in your awesome career and simply comment on this post if you have further questions.