I live in Louisiana, pretty humid here, and keep my fabrics on shelves in an open closet (no door). We have an A/C in the studio and I keep it as cool as possible so that it removes the moisture as much as possible. I don't really do anything else except try to keep fabric stored so they aren't in plastic bins. However, I do have some in closed up plastic and it's been fine. I've been quilting for 20+ years and have old fabric from my mom that may be 40 years. So far I haven't had a problem with mold or moths (although mom's stuff did smell musty but washing took care of that). If you're still concerned, visit an LQS once you get there and ask if they or their customers do anything special about the humidity.
Oh, and good luck! Enjoy paradise!