Hard case. All day long.

Wall hanging or floor stands depends on who and what you have crawling around at floor level that can knock things over. The Hercules and Fender stands that hold the guitars by the neck are pretty stable.

If you use a wall hanger, try to mount it into a stud, or on a horizontal board mounted into studs if you're putting up multiple hangers.

There's also been a rash of non-String Swing wall hangers breaking recently, so I'd stick with the String Swing brand.