There's a reason why "fedora" is used as an insult; wearing one indicates a lack of social skills insofar as the wearer doesn't understand the value of dressing like other people.
At most, there might be exceptions for headgear to keep warm in cold climates, and for regional differences in clothing (such as cowboy hats in rural Texas).
Experience-altering chemicals suggest -very- strongly to me that hats change your perspective and make you feel more sheltered and protected, as well as less personally involved in the situation at hand (reducing social emotions, such as empathy). I'd guess hats are worn by people who lack social skills as a kind of self-medication to help alleviate their anxiety, rather than because they don't understand normal people don't wear hats.
For years, I've taken being a classic nerd, geek, and hacker as a point of pride - eg, consciously trying to judge people by the code they produce, or whatever else they write, as opposed to judging them on their appearance, to the point that I prefer /not/ to know what my favourite authors look like. I've tried to make what strengths I can out of the resulting weaknesses, such as reducing decision fatigue by keeping a single hair-style for many years, wearing whichever t-shirt is on top of the clean shirt pile, and so on.
I'm no longer satisfied with this. I want to become stronger.
Last month, I bought a dozen button-up, collared shirts... and have noticed slight, but consistent changes in my workflow when I wear them. I want to leverage whatever other clothing-based self-improvements are within my budget.
For some years, I've worn a floppy boonie hat to shade my delicate eyes from the burning rays of the sun. (I've even been seen wearing it with a photographer's vest instead of a daypack while tromping around my hometown.) I'm thinking of trying out the 'Crasche' safety inserts mentioned in the recent Open Thread while hiking far from medical help, which would require a baseball-like cap with a sweatband. Given my proclivity for taking something that works and sticking with it for years, I might be wearing that cap for a very long time.
Thus, a multi-layered question: Which hat should I buy? Which factors should I take into account... and which shouldn't I? Are there any subreddits, forums, or other online discussion groups whose members would be willing to take this question seriously and with only a minimum of mockery?