It's obvious that quite a few people here have never hiked in tropical conditions. What BPL normally recommends for hiking in most of the temperate zones just doesn't work in tropical climates. Synthetic clothing, especially nylon like Supplex, is much hotter than cotton and in very humid conditions always feels clammy, because it doesn't breathe very well. When it is very humid you want the fabric to stay moist so as to cool you down more. In such heat, evaporation is so fast that cotton doesn't stay wet for long at all... that's why most people who live in the tropical rain forest always wear cotton t-shirts these days... it does a much better job regulating your heat than any synthetic can do. I'd recommend having a loose cotton shirt and a synthetic 100 weight microfleece shirt for the colder nights. For pants I'd recommend a 30/ 70 polyester/ cotton blend, not Supplex. The blend stays cooler and dries very quickly. It's still not as good as 100% cotton though. I'd recommend cotton twill most (it was designed by the British for tropical campaigns) if you don't think it's going to get overly cold. Jeans are out... they are too tight and get very heavy when wet. Wear long pants, not shorts... unless you are inured to the sun and insects shorts will make you miserable. I personally do best in knee-length breeches, and cover my calves with a mesh leg warmer if it gets cold.
The recommendation for a towel to carry around your neck for seat is a good one. I use one all the time in the sweltering summers here in Japan. You use it for wipe your face while walking, but also to protect your neck from the sun and to dip into streams and cool off your head.
I'd actually recommend sandals for very humid rain forest conditions, but if you have worries about stubbing your toes on the rougher trails, a light, mesh shoe as Ben recommends works best. I personally always wear Chaco sandals when walking in rain forests. THey dry fast, your feet don't get subjected to getting waterlogged in closed shoes and developing fungi, and you can just rinse them off at streams. At night I wear a neoprene bicycle shoe cover over them to keep my feet warm.
For drinking you might want to bring rolls of newspaper to roll your water bottles in and keep the temperature of your water bottles constant... even ice will stay solid all day long.
Leeches will be a very big worry everywhere, even when you sit down to take a break. They'll come looping across the forest floor like things out of a horror movie. You may want to use puttees wrapped around your calves to help protect your legs. They work better than gaitors in such conditions because they hug the contours of your legs.
And though it sounds funny, you might want to get a straw, short brimmed hat. Straw hats are coolest in very hot weather, do quite well in light rain, dry very fast, and protect very well in direct sunlight. And with a short brim they won't get in the way in heavy undergrowth.
The suggestion for a ID Silcape is probably the best. Many mountain marathon runners now use short ponchos in Europe for summer running. It will keep you dry and warm, but also ventilate well. You DON'T want to be hiking in a waterproof rainsuit in the tropics!!!
And finally make sure your shoes fit well and won't easily come off in deep sucking mud.
Also, for comfort, you might want to bring a very lightweight simple hammock. Very useful when you want to rest and the ground is sloshing in mud or the hill is steep or you want to get away from the insects.
PS. If you do bring synthetic clothing to wear, make sure it is very loose-fitting. That way you will feel less baked in the heat.