I solved this by purchasing a vintage display case and using picture stands of various sizes to prop up items. I rotate card themes through the case occasionally just for fun. The other great thing about a large display case (if you have the room) is you can include companion pieces to liven up your displays. I like to try and pick up wrappers, boxes, advertising, etc. that complement my cards.
Here are a couple I've done in the past.
Jim Thorpe / Red Grange Display
Wheaties Display
jeff