For tarpon, you will obviously want to apply different standards, and a basic selection of 1/0, 2/0 and 3/0 flies in a variety of colors will cover the majority of situation encountered just about anywhere in the Caribbean (outside of the Florida Keys!)
First off, make sure that your tarpon flies are tied on super high-quality, chemically-sharpened hooks. A razor-sharp hook point is essential for penetrating the rock-hard mouth of tarpon. We are big fans of the Owner AKI hooks and similar models from Gamakatsu.
As a very general and simple rule, you can fish dark colored flies (black, purple, brown, etc.) on cloudy, overcast days or when the water is murky or stirred up from the wind. Fish brightly colored or light-colored flies (white, yellow, orange, chartreuse, etc.) on sunny days, when the water is clear, and when the visibility is good.
You will also want to have a handful of smaller tarpon flies that are tied weedless for fishing in and among the mangroves. Be sure to have a couple of white, red and pearlescent surface poppers as well.