What is the recommended way to store this mat?

I always unroll my mats and stand them up in a corner. I don't inflate them but i do go out of my way to make sure that is is rigid enough to prop up without folding. Propped up behind a tall dresser of similar piece of furniture seems like a good way to allow it to keep it's shape while in storage and has worked well for me so far.

Because there is no foam, it is perfectly ok to store the NeoAir in it's stuff sack. The only perceived concern really is weakening of the material where the pad folds. Creases are a topic of many gear shops techies as they describe how not to store a tent, etc, but because of the quality of coatings Cascade Designs use on all of their pads, the coatings most likely will withstand decades of folding and usage. I would recommend not storing it in places where there are really warm temperatures (i.e. trunk of a car or in the car period). A gear closet in your house or room would be the best option. Heat is the biggest enemy to any nylon coated with silicon or polyurethane.