I like to store my papers vertically. With papers stored upright, each sheet is easily accessible, and it's simple to slide an unwanted sheet back into its sleeve. Use rigid containers or dividers to avoid creasing the papers.
Consider placing the vertical storage containers on an adjustable bookshelf so you can minimize the amount of wasted space between shelves. Warning: Paper stacks can be heavy, so don't put too much on one shelf.
As inexpensive substitutes for upright shelf dividers, consider stackable plastic sorting trays found at office supply stores. They're designed to hold 8-1/2 x 11" paper, and stack on top of each other. Stack them vertically side by side and use packing tape to attach them to the back of the shelf for rigid shelf dividers.