Your humble question: What classes are necessary to take in high school in preparation for this career?
My humble answer: Rather than taking particular classes, I think what's important for you to do in high school is to learn how to discipline yourself to do good in school and get good grades. From my experience the people who fail this program are those who lack discipline. Other than that, some basic classes you can take in high school that will help you get through this program are basic physics, chemistry, math, and any health related classes. Another thing I'd recommend is participating in a shadow program if your school offers such a thing. Where I live the local high school has a healthcare shadow program where you participate in a class to learn the basics of healthcare, and then you shadow the various medical professionals in the hospital such as respiratory therapy, nursing, x-ray techs, lab techs, pharmacy, etc. Any of the above will prepare you for RT School.