I used to play every controller game with thumbs on sticks/buttons and index fingers on the triggers/bumpers. When I play smash now, though, I feel the need to have a finger over Z at all times, just in case. So although my left hand hasn't changed (thumb on stick and index on L), my right hand shifted so I have my thumb on the buttons/cstick, index on Z, and middle finger on R. I don't use R for anything, even wdoos, so I think I just rest it on R because it's more comfortable.
I have a friend in college who plays left hand like mine, but rests his controller on his leg, not gripping with the right hand at all. He uses the buttons and cstick as if they were keyboard buttons. It's a really interesting style since you can use multiple buttons at once, but unless you start from scratch learning that way, it doesn't seem worth it.