Am going to Panama during the rainy season with my kids. What should we wear/take to be comfortable in the humidity? What kind of shoes? umbrellas? How do we avoid mosquito and chigger bites?
Rainy season means both hotness and high humidity; the high humidity is the reason why people feel so uncomfortable because our main defense against heat is the cooling caused by evaporation. High humidity means the air is already full of water vapor, so it does not work well during rainy season.
So clothing should ideally be able to exchange humidity well: be absorbent and still drying fast. Cotton has the disadvantage that it stays wet: This is not a problem if the sun comes out and you can dry it, but let's have some rainy days (mountains, rainforest) and you cannot get the humidity out: It feels clammy and it tends to get easily mouldy (the climate is ideal for fungi and microbes).
I suggest you try linen because it feels cool, it is naturally very dirt-resistant and germicidal. Ok, it wrinkles easily, but it feels good on the skin. Some people are complaining that it feels too heavy for them, so try it out yourself. While not so good, I also recommend hemp which is also cheaper. If it is sunny, silk is also an option. I am also using expedition trousers with zips and shirts which are mainly polyester, they are very comfortable and drying easily (if you do not mind the Look-this-is-a-tourist feeling).
Oh, and do not forget: Shake clothes and shoes before wearing them because small animals are using them as hiding place in the night.
Shoes: Sandals, Sandals, Sandals as much as possible, your feet need respiration. If you go into the rainforest, you need to protect your feet, not because of snakes, spiders etc. but because cuts and rashes are easily infected and heal badly. The best shoes for rainforests are (sorry for mentioning them explicitly, but they are really exceptional) Haix multifunctional shoes. Also an option are rubber or combat/Gore-Tex boots: While perspiring, they are still comfortable enough.
Rain: Tropical rains are not comparable to "normal" western rains. If it rains, IT RAINS. I mean, REALLY, REALLY RAINS. So most travellers simply use a light and watertight jacket or poncho if they do not find shelter. I do not know if you can use an umbrella, but I think it will be uncomfortable because you must hold it firmly. You will also see why sandals are best because they don't mind to be flooded and the rain is warm.
Mosquito: Mosquito net. This is a must. I recommend to sleep in a hammock because you have no problems with small animals visiting you in your bed, it is very comfortable and your back stays colder and less wet. For repellents either use Icaridin or DEET.
I just got back from Panama, and while it technically wasn't yet the rainy season, it was getting there. Here are some thing that might be helpful.
Our dress was to wear what you'd wear for hot climates - shorts, t-shirt, hat - and also have a lightweight rain jacket handy. In the end we never needed the rain jackets (we were close enough to shelter the few times it rained) but for us the rainy season hadn't really started. Shoes should depend on what else you are doing. If you aren't hiking then sandals works fine. If you take an umbrella, make it a sturdy one. When the rain comes it can be really hard.