We've tried several storage systems over the years and the best way we have found is:
1) Pallet Racking for bulk storage of media (we tend to order pallets of popular vinyl such as 3M 40C and 3M SV480mc). Or even just two or three rolls of a specific product.
2) When not using popular media store it in it's box back on the pallet racking
3) Some media's we print rolls of almost daily, so we keep close the printers on these carts:
https://stock-and-roll.com/en/products/stock-and-roll-6-bobines
The reason we like these the best are they store 6 rolls of media without the possibility of toppling over if you bump them, they roll easily but can be locked to not roll, and they are circular so you never media stuck in the "middle" of other media like you will have with the
mobile vinyl racks that were referenced earlier (if you have large rolls you need to access stored in the middle of the cart, it's a huge pain in the ass).
If you wanted to do something more stationary like
jfiscus posted earlier with the rolls of media along the wall, I'd recommend the podium from Stock & Roll - as it provides the same concept but makes it easier to access media stored behind other medias.
https://stock-and-roll.com/en/collections/podium
While the product is expensive, the pricing typically includes (or at least it has when I ordered them before) shipping from France. If you contact support Marie will probably respond and mention Matthew from DSGI made the recommendations and she can help you find the right product (or products we've ordered before).
Full Disclosure - I don't get anything from Stock and Roll, I have no affiliation with them and I have paid full price for everything I have ordered, I'm just a happy customer.