and my solution is just get rid of all of that stuff and then...no need to store it. but i understand some people wrap gifts as a hobby...creative expression...stress relieve...in that case...there are your supplies!
Storage Mistakes You're Making (and How to Fix Them)
Even narrow closets or cabinets can quickly become a storage nightmare, with a hodgepodge of items with no order. Luckily, bins, containers, trays, baskets, and the all-important labels can quickly restore storage calm. Subdivide by color or type of item, and label shelves, too.