As per #5, you'll need a number of hats. Unlike as per #5 and as per #1, I have no natural protection.
For sunshine non-smart use I have a Tilley, and for smarter a fabric lined straw hat. Not a proper Panama - they are ferociously expensive, and if theyre not they will fall apart.
For wet weather use Ive got a waxed cotton Tilley (again not smart, but works very well), and for smarter a water repellent Fedora from Orvis. Bought the Tilley just a tad too small so that it stays on when the wind blows.
Drizabone is another good make.
"country living" fairs/outdoorsy shows/agricultural shows are handy places to go to find different sellers in one place.
When its cold I wear a beanie (Dickies do a Thinsulate one at a good price) and stuff what anybody thinks it looks like. Their problem, not mine, as I cant see it and Im warm and cosy.
Also I have a bump cap for when I'm at risk of knocking/scraping my head. If youve not found yet, (you will) quite minor encounters with, say, loft timbers, which would be no problem at all if you had hair, will give you an uncomfortable graze.