I, too, live in a climate that can be uncomfortably warm and have to use an eye for cooler fabrics. For 3 season wear, I lean towards a linen jacket, and to match my style, my current favorite is a light tan linen jacket (the linen adds a hint of texture I love) that looks damn good with dark denim as well as light chinos. If i were in your boots, that would be my next purchase. Partially lined, light in color, hint of texture, linen; while not linen, Banana has a two button jacket made of egyptian cotton that otherwise fits this bill. Then I would consider acquiring a grey suit, light grey, whose pants could be utilized alone without looking like it's missing its other half.
As other's have suggested, shoes, shoes, shoes. The old advice still rings true: shoes will make or break even the otherwise most exceptional of outfits. For the arid areas with rougher terrain, you can of course go with the traditional Alden or Allen Edmonds boots, or you can give RM Williams boots of Australia. I just picked some up recently and am very pleased. Best of luck!