There are sooo many ways to organizing your wrapping supplies! There are many, many products out there to help you. Obviously the way you organize depends on the space you have available.
Here are a couple before pictures of a project I did. The client and I decided that just putting things in boxes and then putting things back on the shelf would probably work best with the space she had.
It is really important to measure your area BEFORE heading to the store. It will save you having to make multiple trips to the store before you have all the right containers!
You of course want to label all your boxes so items get put back into their proper containers.
16 Quart Boxes are great for the large rolls of ribbon that you may get from Costco. Just make sure that everything has a lid. That keeps things neat and keeps things from oozing out of their containers. No Oozing please!