In one of the guilds I belonged to they had two different instructors one right after the other. The first one says she cuts her bindings at 3 inches because she likes them as the final framing and if you're going to go to all that trouble they should be seen. So then the next month the instructor says to cut your bindings at 1 1/2 inches so they're very narrow and not as noticeable. But both of them did say they use straight grain binding unless the quilt has a curved edge.
I think you can do pretty much what suits you and what suits the quilt.