I supply the playpens. My husband installs terry cloth covered ply wood bases instead of the ones that come with the playpen as the plastic insides will crack and break over time. I then put on a crib sheet, thick comforter and an additional thin blanket on top for cushioning and then a blanket to go on the child for sleep.
I would not use the air mattresses as I would worry they might deflate and become a suffocation hazard.