Vertical is the best!
I have found that I cannot get to my 12 x 12 paper as well if it is stored horizontally. I tried stacks and even bought some of those 12 x 12 containers that are about 5" tall at Michaels. I am convinced that the best way to find the paper I want is to store it vertically so you can see each sheet. My 8.5 x 11 cardstock was in this old black plastic pendafile box...I moved the cardstock to a filing cabinet, and all my 12 x 12 paper is standing up, within reach, and filed by color. The SU sets of paper were easily kept together by filing them in the predominant color's place. I put the dots and lines paper in the front, then the light shades, followed by the darker shades, and then finally, the solids. My small scraps are in a separate place, but larger scraps are paper clipped to another in the file. It is working for me so far.