I lived in Latin America for a couple of years, mostly Panama which is VERY hot.
I lived in natural fibres; good quality and very light linen, cotton and silk. Never ever ever polyester.
A good quality pair of white shorts, a plain skirt, a couple of silk shirts. T-shirts for more casual days. Floaty dresses in light cotton.
One of my go-to looks is quality cuffed white shorts with blue and white striped shirt.
I bought 3 silk shirts with collars from Lily Silk, they last forever, you can really dress up anything with them and they're so light and breatheable.
As for a bag, as a tourist I'd put cash / cards into a waist belt underneath my skirt / shorts, then hold a tote with necessary things like water, tissues, stuff that doesn't matter if it's stolen.
Hat, sunscreen.
I always wear makeup and it is harder in the tropical heat. My skin is also oily. I lived with oil blotting papers always handy. I also applied loose translucent powder with a dry sponge, carefully pressing it in all over, to set. Brushing off excess after a few minutes. This made my makeup last longer and I got oily less quickly.
I've found a proper tubing mascara a game changer. Normal mascara runs and my oily skin made even waterproof mascara smudge. Tubing mascara never smudges or runs and it's so easy to remove.