This article does a great job breaking down what kind of hat you should get for your face shape.
Make sure the hat you choose doesn't overwhelm your features and highlights the better ones.
You also don't want your hat to elongate the wrong part of your face or make your head look weirdly shaped.
So follow the advice in that articles.
One problem with the article is that basically every type of face they recommend a fedora, and sadly fedoras are totally douchey right now thanks to some pickup artist types who started to wear them.
So avoid fedoras.
And really obviously "statement" hats.
But hats are cute and can make you look different, and also keep your head warm in the winter, so get one but make it the right one.