...a flatcap.
Of course no hat at all is safer, but if you must wear a hat a flatcap really is your best option. I'd caution against wearing them with a suit though, unless you're actively going for the turn of the century Irish farmer look.
Nobody over the age of 16 should ever wear a baseball hat unless you're actively playing baseball, and nobody should ever wear a trucker hat. Not even truckers. And god help you if you're one of those cunts who put a fucking fishhook on your hat.
Fedoras are obviously right out of the question. You definitely do not look like Humphrey Bogart. You look like a twat.
Stetsons are acceptable if you're actually a cowboy, but are otherwise best left alone.
You're welcome. Don't worry, I won't be charging you for the advice.