Gryffin, alas, baseball type caps and umbrellas are no good for me because of the aforementioned photography thing -- turning the camera vertically causes the camera to bump into hat brims (so any brim needs to be really flexible (i.e., not stiff so that the cap tilts back on my head) yet not floppy. The one I have is kind of like this:
https://www.rei.com/product/11.....rimmer-hat
Not stylish at all but useful for a long day in the sun when I'm in gear.
When I go running or hiking with no camera gear, I'll wear a baseball-style cap. Rain or shine, since it keeps the rain off my glasses as well as sun off of my face! I do like the idea of the one with the sun flap, and good to know it fits a small head, since I am of the small noggin club too.
Umbrellas are a total non-starter because I need hands free for camera gear. But thank you for all the info! I have a pretty good sunscreen routine.