Define expensive, and define cheap please.
The one I know of that is quite reasonable for self-storage is Zebrabox, they have a number of places throughout CH, including Basel. http://www.zebrabox.com/en/
If you are using a moving company, I've found that adding on storage costs to the move are often not prohibitively expensive, as the company has storage facitilties and easier than using a middleman.
Other than that, find a farmer, and see if he'll negotiate storing your stuff in his barn.