Stampin' Up!® Ink Pads need to be stored flat so they don't leak. I would recommend that you store ink pads flat regardless of the brand. There are many ways to store ink pads from stacked on a shelf, in a container, using stacking systems for other items (think DVD/Video storage) or modular and custom built solutions.
This article looks at a options from budget through to modular options. Custom built options are available from cabinet makers or the handyman in your family/friends circle.