Hi , given your budget the DA 55 - 300 would be your best bet. This lens will be able to deliver in 90% of the time under good lighting condition.
Just take note that this lens will probably struggle when you attempt to take headshots of the mandrill at 300mm f/5.8 ( esp. when the mandrill is sitting under the shape ) . I think even if you fire the flash, may not help, considering the distance between the subject and you.
Otherwise this is a value for money lens, considering the size, focal length and price. Happy shooting at the zoo .