I've had a few favorite hot-weather hats over the years. I guess my all-time favorite was the "up-downer" style hat that Lefty and Mark Sosin helped popularize. That hat was very functional and was the trade mark of a saltwater fly-fisher - gear anglers too. I preferred it with the standard length bill, not the long one you see today. The long bill doesn't give you that much extra sun-protection but it does restrict your ability to see your line loop sooner, making casting accuracy more difficult.
I've never liked the hats with flappy stuff hanging down the neck and coming around the face. When the wind blows 10 mph or more, the flapping against my face and neck drove me nuts - plus the noise - I couldn't hear my guide clearing.
The best hat I've ever used for just reflecting heat and protecting my face and neck is the Sun Tamer Hat by Pro-Trim. This is a Vinyl (something) hat with a web head band. This hat reflects about 95 percent of the head and the web band lets air continually circulate around your head. It has a chin cord that can be worm a couple of ways to keep the think from blowing off even when running fast. It's also a very good-looking hat.
I don't wear the Sun Tamer to fish in anymore but I do where it when I'm gardening. I don't wear my Up-Downer hats either and I have at least a half dozen of them; some new. Once Buffs came out, I made the total switch to baseball caps and a buff. The combo pretty much provides total sun protection and with the back of the Buff pulled up over the back of the hat, it won't blow off in a strong wind or when running.
So, my favorite hot weather hat is a ball cap in concert with a Buff. No flapping going on either. That said, you can wear a Buff with any hat, including the Sun Tamer.
[click here to display pictures]