You can't beat a Stormy Kromer hat. I've got three...an olive green one, a blaze orange one and then a green/black plaid one that has the Goretex lining.
I'll warn you right now, DO NOT get the Goretex lined Stormy! It's way too hot for me, even in the coldest Indiana temps. Get the standard, unlined Stormy in your color of choice and you'll never be sorry.
All of my hats have the normal sized bill. I just turn the hat around backwards if I'm bowhunting with it on. Friend of mine (aka "German Dog" on here) has the brimless Kromer and likes that for bowhunting.