You might look at volunteering at one of the shelters. I know the Animal Defense League has a great volunteer program. Or possibly even working at one, I don't know how old you are . Another place you may look for work is at one of the Doggy Daycare Facilities. I take my dog to Lucy's Doggy Daycare on Thousand Oaks. They also have a Downtown location and one out Northwest. There is also a program that uses horses for therapy for people with disabilities. It is called Saddlelight, I think.
Beyond the traditional jobs, such as veterinary or zoo type jobs, there are many others. One that comes to mind is environmental sciences, where you would do research to help protect endangered species, such as how to improve their habitat, or even legal work where you would try to stop things that are endangering animals. . . .say like if wind turbines are killing bald eagles, what do we do?
As for schooling, I recommend a strong science and math background for traditional animal care jobs. If going in another direction interests you, say like pet therapy or legal programs, you would need to add other areas for those. While in HS, you cannot go wrong if you challenge yourself as much as possible. For example, speech class, because you do not want to find yourself in a position where you are underprepared for later life choices!
p.s. also look at the school's FFA program!!