Surprised no mentioned it already, Tilley hats, lots of styles, water resistant, great for fishing. I have one that looks like this.
I too would of passed on your baseball cap. I wear the tilley hat in summer to keep my ears from getting sunburned. Of course if you have long hair the sun might not get to you ears. If its real hot out I just dip my hat in the river and put it on my head, helps to cool things off.