We decided to refloor our basement with carpet tiles. That way, if we ever had another water problem we could possibly save the flooring ourselves. Also, using random carpet squares was very cost effective at a dollar a square foot and dead easy to install without any surface preparation other than a good vacuum.
Our basement stuff, unfortunately, was simply piled up and that pile had to move about while the floor was being laid. In the end, most of that material ended up in one location, ready to be either stored or dispositioned.