My 12 x 12 Cardstock is stored for the most part, in these paper trays which used to be made by Display Dynamics. They were discontinued but you can get similar paper trays by Umbrella Crafts from Scrapbook.com.
I split them up into groups of five and store mine in my Ikea Expedit Unit.
You will notice a wire tray on the left side of my Expedit. Those were given to me by my BFF and I’m pretty sure she got them at a store sale. I have noticed that My Mind’s Eye has a similar 12×12 wire paper tray on the market now that is very inexpensive and that looks like this:
I do have some other cardstock that I store in a hanging file cube from Michael’s but I do not recommend it. It’s not made very well and I’m in the process of replacing that cube and moving that cardstock over to my paper trays.