Rain gear

Asia tends to be hot.
You get wet, the sun dries you.
Buy a brolly

Agree, because rain gear is impervious no body heat can escape and you will be wet inside the clothes anyway. So most people have an umbrella or wait until it stops raining - different pace of life in the far east because of the climactic conditions. Note after rain, rising water vapour after the sun comes out is a killer - 100% humidity for a short time.

When it rains, most just take shelter, especially when there's lightning, and wait until the rain stops or lightens.  As previous posters have mentioned, it's hot here in the Philippines. What you would need is an umbrella or a rain coat if it's rainy and windy or if you drive a motorcycle. No need to bring rain gear from the US. Just buy an umbrella and rain coat here.

Rain here can be just droplets to buckets of water (like during the typhoon Ondoy in 2009). You will experience the different rain volume once you live here continuously for a year or more. And depending on where you plan to reside, water can rise fast and your house can get flooded. In that case, a second or third floor at your house / apartment is what you need, plus muscle power to haul things upstairs, rubber boots and a shovel (for mud), and a flashlight.