I hold mine on my back. Every trip I've ever been on, I've only ever needed one backpack. I was raised to travel light. Never, ever had to deal with baggage claim.
I roll it behind me, I don't see any other way unless you have one of the bags with 4 wheels but even so I think i'd pull it behind me since I find it easier that way
I don't travel, so I have no need for luggage. However, way back in the day when I used to visit a boyfriend who lived 3 hours away, I used duffel bags. I voted for "beside" because I didn't drag them on the floor; I carried them.
Behind me or on my back. If I am flying I will check it in. DO NOT be one of those people who somehow sneak four carryon bags on the plane and take up all the overhead and foot space. Kills me.