I bought two $15 book cabinets in boxes at Walmart. Once I assembled the cabinets, I bracketed them together back to back and installed my tabletop press on top. They have lots of storage room and two adjustable shelves on each side. I put the backs on the cabinets so they are divided, but you could leave the backs off so you have more storage from one side through the other. The thin MDF backing is what solidifies the cabinets, so if you leave them off you would have to brace the inside corners across the cabinets with 1" x "1 and drive screws through them vertically and horizontally.
I'm in the middle of moving, so the press is packed up.