The only time I cut my packs of paper is if I bought them specifically to mass produce a particular card for Christmas cards or some other occasion. If I'm buying the paper just to have on hand for future projects, I don't cut ahead of time since I use it for more than just card bases, like making 3D objects (boxes, etc.) that might require the entire sheet.
For most of my cardstock, I store them in black Sterilite file boxes.(Sterilite - 1871: Portable File Box
The room most of my 8.5x11 cardstock is stored gets a lot of sun and if I don't have it in something dark then it tends to fade or change color. I like the smaller containers because if I use anything bigger (since I need something portable), the container gets too heavy to move very often.