Wrapping paper can be an absolute bear to store unless you spend plenty of money on specialty storage containers. Well, why do that when a cheap kitchen stool from the salvage/thrift shop/garage sale can do the trick just as well?
To make my life easier in the end, I add 4 casters (from the home improvement store) to the top of the seat. Then I flipped it over
I used a couple of old pillowcases to create different sized storage bags to attach to the rungs using double-sided velcro.