When I had my dog, I got one of those large, black floor mats/rugs. It was about $30 at Target. They are the ones you see when you enter shops, Dr. offices, etc. That helped a lot. I was really surprised.
I also think you'll need more than a Swiffer. I got a mop at Home Depot. It's a sponge one. I think the ones there are a bit more hefty.