Ball hat of some variety. Visors are out, because sunburn on the top of the head is a painful, distressing thing.
Used to have an old Greg Norman "Shark" hat, but I just found it too large.
I'll play without a hat in May or October, but not often.
I felt that way, too, but continued sunburn on the back of my neck & ears (and all the posts here about taking skin cancer seriously - this is the real reason) I decided to switch this year to an Aussie Chiller hat:
I quickly got over the size of the brim, & it feels kinda natural now.