What high school classes do you need to become a vet?

You should focus on taking the most challenging science and math courses that you can handle - physical science, Biology, chemistry, physics, calculus, statistics. All of these courses will be repeated with more in-depth material in undergraduate college (in the United States), so you need a strong foundation.
Take as many science courses as you can, preferably the advanced or college-prep courses if you can. Take as high-level of mathematics as you can - if you can get all the way through Calculus I in high school, your undergraduate pre-requisites will be much easier.

Other than this, take classes you enjoy - vet school doesn't work out for the majority of people who go to college to become a veterinarian. Explore other paths as well, and take some classes you enjoy if you can.