On hats:
Popular hat styles for men include caps, fedora, cowboy, toque, beret, and flat cap (aka driver's cap).
First of all, a baseball cap is properly worn, if one must wear them, with the bill forward, as it was designed (to keep the sun out of a baseball player's eyes). Habitually wearing them backwards outside of the age of college boys is saying to the world - hey look, I'm an idiot. Thanks for the warning, though. I do appreciate that part.
A fedora is a hat style. A Stetson is a brand, its style is 'cowboy'. Get it right. And while I'm on the subject of personal dress and misuse of terms, 'khaki' is a color - the pants style is called 'chino'. One has a pair of chinos in khaki, not a pair of khakis. And the beard style so popular with geeks and nerds is not a 'goatee' but a 'Van Dyke'. A goatee does not have the mustache connected to the beard. A Van Dyke does. Again, get it right. OK, end of rant there.
The best fedoras are properly made by Borsalino. They also make very nice flat caps.
Because I am an uncouth American with very little sense of style or fashion, I normally wear a baseball cap, and when I am about to turn my camera lengthwise to portrait orientation, I spin my baseball cap around and wear it like a lout.
In the winter in Michigan, I often have to wear a touque. No worries, my wife knitted it for me from Alpaca and it is quite warm. No brim to get in the way of the camera.
I have a nice fedora and a flat cap, both made by Borsalino, which I wear when it makes sense to do so.
I am quite bald, so wearing a hat is more-or-less an imperative.
I would not wear a beret if I were given the choice between it and a painful sunburn on top of my head. People who wear berets by choice (and not as part of a military or police uniform) should be shot out of canons into the nearest large body of water.
All other hat choices are acceptable. I wish the fez would make a comeback. I look stunning in a fez.
My list of baseball caps is quite large, but I prefer the khaki-colored one which I got at Gettysburg College, which lists the name of their sports team - the Bullets. It gives peaceniks conniptions, which is just a positive for me.