I have several ball caps, find the bill cuts down on glare, rain off my glasses. When I really need protection, I go to my ventilated crown Tilley, brim is supposed to be spf 55, very comfortable and also washable.
I dunno why, but when I was a kid I thought hats were cool as can be. Now that I'm older I realize they just cost a lot of money if they have my steelers logo on them and end up all sweaty in in summer.
Due to some "dome thinning", my dermatologist has recommended a hat for extended sun exposure, which I get a lot of in our pool and in Aruba. For garden work and walking, a straw hat protects without over heating. In winter I prefer leather Australian Outback style hats for protection from rain and cold. I rotate among some seven hats.
My straw hat kept my head from being parted yesterday not ducking low enough from a branch while mowing. Now it's time to look for another one as it got trashed.
I never wore a hat prior to moving to Arizona. I learned quickly it was necessary here. I have an assortment depending on season and weather. I never go out without one.