Well, think wet, warm, and humid. Nothing you wear as a rain coat is going to be all that comfortable, so I wouldn't spend a ton. Marmot's PreCip Rain Jacket ($100) is fine. It's light, packable, and reasonably breathable. Patagonia's Rain Shadow ($150) is a little spiffier, with Patagonia's reliable H2NO coating and a little better detailing than the Marmot. Outdoor Research's Rampart ($89) is completely waterproofand also coated, so it will not breathe well. But for low-exertion activities its fine.
The other thing to do is take an umbrella. Seriouslythat keeps the rain off nicely!
For footwear, you might start with the Vasque Synergist ($130), a lightweight boot that has a Gore-Tex liner for waterproofness. They'll also dry quickly once theyre wet. Garmont's Flash 3 XCR boots ($140) are very similar. Take several pairs of socks so you can swap out dry ones. Wear REI CoolMax sock liners ($5) as a base layer, then a pair of Thorlo CoolMax Light Hikers ($16), which are made for warm weather and dry quickly.
Underwear? Anything light and synthetic. Lowepro's Men's Briefs ($18) will do nicely.
And, for a hat, Outdoor Research's Transit Sun Hat ($29) is light and airy, and it dries fast. Just the thing for hot weather.
Hope you have a great trip!