The snap brim means that the front is pulled down with the back up. Some people wear a fedora with the back down in a sort of outback style (called a turn-down), but that just looks crazy. The brim on this fedora hat is 2 1/2" (which is the brim size Bogart wore).
If the brim is less than 2", it's called a stingy, and was popular in the 60's. A 2" brim or less is the fedora hat that Frank Sinatra is known for.
A 2 1/2" brim is the most common in the 40s, like the one Bogart wore.
If you're getting a 3" brim, that's huge, and is more like a zoot suit type fedora hat.
If you are going for a specific time period, you'll have to wear the brim size they wore (about 2 1/2" in the 40s, down to 2" or less in the 60s).
If you are somewhat flexible, though, big men look best in wide-brimmed hats, thin men look best in narrow brimmed hats.