If it were me I would use a oil based stain last longer on wood then paint.
But if you have your heart set in latex paint I would use a good oil based primer then use Sherwin Williams A-100 or Super paint.
STAIN it.........paint will give you maintenance headaches for years to come..........especially in South FLorida. You can use a solid color stain or semi-transparent. Latex stain would be fine for your fence. Check out Woodscapes from Sherwin-WIlliams.