Hi Mustafa! I know I was definitely someone who wanted to get as big of a headstart on getting into vet school as possible, so I also started thinking about these things in high school. While it was helpful and enjoyable for me to start getting involved with veterinary and animal work at that time, Bottle of Bear is also correct in saying that it's okay to worry about high school now and vet school later. It all depends on what works for you!
That being said, to be a veterinarian you have to go to an undergraduate college for at least a few years (most people go for ~4 years and earn their Bachelor's, some go on to do Master's or even PhDs before vet school), and then you have to go to an accredited veterinary school for another four years. At a minimum this will be around 8 years of schooling, and afterwards veterinarians often do additional internships/residencies for a few years if they want to specialize.
While you are an undergraduate student, you can study just about anything you like as long as you still fulfill all the prerequisite courses for the vet schools you want to apply to. This can vary from school to school, but usually includes at least a couple of semesters of biology, general chemistry, organic chemistry, biochemistry, physics/math, and English. Your best shot for acceptance and a more affordable veterinary education is at your in-state vet college (if you are from CA, then these would be UC Davis and Western) so those would be the best places to go looking at what you'll have to take in college.
Their websites should also have information on the average GPA of accepted applicants, as well as average GRE scores (a standardized tests that vet schools ask for, kind of like the SAT). From what I remember, that GPA was usually around a 3.7. Veterinary schools will not look at your high school GPA, so right now you should be working on getting the best grades you can so that you can get into a good undergraduate college/get a good scholarship for undergraduate. It does not matter where you go to do your Bachelor's, but keep in mind that vet school is very expensive, so you should try to minimize the amount of money you'll spend on undergraduate as much as possible. For some people this might mean doing something like taking some classes/prerequisites at a local community college. You don't need to go to Harvard to get into vet school! Veterinary colleges also like to see research experience on applications, so any school that would allow you to do some of that would be a plus.
Finally, the average accepted veterinary applicant usually has around 1000 hours of veterinary experience (working directly with a vet) AND another 1000 hours of animal experience (working around animals without a vet present). I had a very hectic undergraduate schedule, and I was always very thankful that I had done some of the work getting my own experience hours while I was still in high school. While it is true that a lot of places will not let you volunteer until you are 16, I was able to volunteer walking dogs at a local animal shelter with my dad and to work with zookeepers at my local zoo before I was that old. Try looking for animal volunteer opportunities near you and see what comes up! Vet experience may be a little trickier since there are liability issues involved, but a practice that I worked at allowed people as young as middle schoolers to come shadow. Ask your parents to drive you around to local clinics so that you can ask about shadowing opportunities; dress professionally, ask politely, and see what happens!