A USPS flat-rate box worked perfectly, when the top flaps got cut off and I split it down opposite corners. The bottom flaps were aligned and taped together, then the short flaps cut from the top became the ends of the box when it got folded together. Then I covered it with fabric, previously purchased at a thrift store for 99 cents, and stapled/hot glued the corners. The staples weren't quite long enough, so I found some little pearly-colored glass bits and glued them over the staples. The basket now slides neatly on the short shelf under the upstairs computer--which was also just replaced. I need to finish clearing that room out to accomodate the traffic it will now get.
I feel so domestic! I even washed dishes today!