My friend, if you can somehow eliminate that expense, do it. The sooner, the better. About 20 years ago I rented a storage unit for several years and after finally leaving it, I found out that i could have purchased what was stored several times over with the money that had been spent. Rather than store the empty boxes, toss them or even sell them on Ebay and at least move to a smaller and cheaper unit.
I wish we could! The real problem is that the house we're renting is crazy small and the storage unit is also full of other stuff we use pretty regularly. What we need is to move to a bigger house. We were planning to start looking for a place to actually buy, but the pandemic craziness and uncertainty has pushed everything further down the road a few years at least.
But honestly, what I need to do is to sell off part of the collection, not just the boxes. But that prospect is almost as daunting as buying a house!