A flat file cabinet is your best bet for long term storage. Check your local craigslist listings or Amazon.
On the cheap end of the spectrum, I think it's worth checking out an art portfolio bag. The size options of these bags are limited, which is really the only caveat I can think of.
Haven't set aside many hard copies of my work lately (most of my sketches/drawings are on the iPad Pro these days), but in college when I was using large sketch pads and printing a lot of things, I used a portfolio bag similar to this and separated the pieces with cardboard and paper.