Fedora: the king of men's hats
Possibly the most elegant hat a man can wear, a felt hat is the definition of a cool man because of his association with gangsters and singers of prohibition at the beginning of the 20th century.
Widely used by Frank Sinatra, the fedora is a soft woolen hat with a central fold and wide brim to block the heads of inclement weather, although it is mostly used for aesthetic purposes.
The folds are for the fingers to close for easy removal and placement. If you are looking for a felt hat in a warmer climate, try the Panama hat. It's the same look and shape, just made of straw for breathability.
The heyday of the felt hat came in the 1960s, since you would be surprised to find any man who did not wear a felt hat in public, including the working class. Most of the hats are decorated with a grosgrain or leather ribbon.
The challenge, really, is to make the hat yours. Like velvet jackets and leather bags, a good hat looks better with age. Use it, return it frequently and use it until people associate it with him.
Remember: put something on once and it's new, the second time it's familiar, the third time it's your signature. Also consider your proportions. You will not be surprised if big hats look better on big heads.