I pull out a sheet when I need it, and order more when the stack gets small, always putting the old paper on top of any new paper ordered. I've found it's sufficient to keep the paper in the original brown paper or plastic shipping wrapper, if the paper is used within a few months of purchase. But flat files or portfolios are safer for long term storage of papers or paintings, and also more convenient to use. The really top end storage arrangements are wood or metal flat files . The drawers are usually 2 to 3 inches deep, which will hold as many as 30 to 80 sheets, depending on weight.
Some retailers also offer stackable trays in the same size ranges as flat files.
These have open fronts, so that you just slide paper in and out. Stored this way paper is easily accessible and largely safe from light, though humidity and homesteading spiders will have free access. Once you've finished a painting, you can store it in a flat file or in a portfolio . But the portfolio is really the thing to protect the work during personal transport. Portfolios come in three basic styles.