Previously, I worked in the Houston Zoo, working as Assistant Supervisor, Primates and also Cats and Bears for 4 years. The earlier you realize you want to work with animals the better. I suggest a college with a strong cooperative work program with local experience working with animals. This is a very competitive field but there are lot of avenues to go down. In my view, nothing takes the place of field work.
Volunteer work is very important.
We have a shadowing program with high school students and college students interested in Animal Science, Biology or Pre-veterinarian specialties. Also young people should be aware that a lot of the job is cleaning up after the animals, there is a lot of manual work. Each zoo is inspected yearly by the USDA - they must meet the minimum requirements. If an accredited AZA facility, which most zoos are, every 5 years they are also inspected by 2-3 people from records to guidance with a very restrictive review of everything going on at the zoo. The AZA tells you at their annual meeting if you passed or not.