I've posted this 'in progress' photo before, but you said you had a wall, so I'm sharing it again.
My husband and I bought a bunch of unfinished upper kitchen cabinets and stacked them along a wall where a full depth cabinet would not have worked
They're about 12" deep - fabric is easy to find, hidden by doors, and easily accessible. Luckily the doors hide the haphazard way the fabric is stored