Ever look at a gun safe from a sporting goods store? Plenty tall, should be about the right width, and they are usually over 200 pounds. Prices hover between say $500-900 for a pretty good quality one. You do have to bolt them down because they are "front heavy," but as said, if you worry about theft, it should be anyways. These sorts of stores would deliver it as well.
Other people here provided great options! I think it certainly depends on what you're storing. If it's a bunch of oddly shaped things of different heights and widths, or if its primarily papers, that will have an impact.
Best of luck!