Still, cover the floors with a drop cloth. Spilt paint will gum up the sandpaper quicker if you don't cover the floor. The drop cloth reduces this problem AND, for what little you do get on any flooring, you can still sand it off.
You can vacume the walls with a soft bristle accessory on the end of a vacume wand. You'll have to do this if you do the floors first because you can't paint the walls if they're dusty. Don't worry about it. It's not a lot of work. You can always use a soft cotton cloth on the end of a bristle-broom to 'knock' down the dust off of your newly painted walls.