For summer nothing beats an Amish straw hat-inexpensive,well made,cool and they look uncannily just like a mid 19th century one-crown flat on top like a boater but a good 1-1 1/2 inches taller with a flat 4 inch brim.If you wet them you can pan dip and kettle curl the brim if you'd like.
The braided palm leaf hats made in southern Mexico and Guatemala are the same way. I have a 5 inch brim one with a telescope crown.
I've got a John B. Setson Panama with a 3" kettle-roll brim & a telescope crown that I've been wearing in summer for almost 10 years. It's called a Rhett--you can guess where it got the name--& it's one of the most comfortable hats I've ever owned. I don't even know if they make it any more. It's a little yellowed from age, but I clean it up every spring. I get compliments on it every time I wear it.