Hat help

[1300cakes]

I've got quite pale skin and get sun burned easily, my eyes are also sensitive so I have to wear a hat pretty much every day. But I've never found one that looks good. I've got no idea about style and no fashion sense to be honest so I need help! What sort of hats do you all wear and what would look stylish (or if not stylish at least as non-weird as possible).

Additional info: I've got a round face and a big head.

I have sensitive eyes and always leave the house wearing a hat and/or sunglasses.

I have a navy fedora type hat made of felt which I wear most of the time. Not the best quality as the brim sometimes flips up in the wind so I want to upgrade a better quality rigid wool one - i'm keeping my eyes on ebay. I used to have a trilby but the peak wasn't big enough to keep the sun out of my eyes and doesn't really protect the neck. For cycling or running I just use a boring old baseball cap which isn't stylish but does the job.

OK I'll look up fedora type hats to give me some ideas. Yep I don't mind what hat I wear if it's for exercise or similar, but I wish I knew what would be fashionable to go with smart/casual outfits.

I like a panama in the summer