The foundation of any stylish hat collection is the newsboy cap. It works because almost no other article of clothing spans all the echelons of society. Everyone from the hedge fund golfer to the, um, newsboy can get away with a newsboy cap. Some people will say that you need to be old enough to grow a full mustache before you can wear a newsboy cap, but this is just people’s 21st Century bias talking.
In addition to the newsboy cap and flat cap, we have the option to wear berets or fedoras. While these two hats are indeed trendy, they are far from stylish. Unless you want people to stereotype you as an ineffectual poet, so if you have to wear a hat at all, I’d stick with the newsboys and flats.