Shipping a box is insanely expensive.
And to 04SCTLS, I don't think plywood would be a good option for a box. I would think something with a more consistency in density would be better. Also, I wouldn't want the box to be completed, turn it on, and have a section of it rattle because of delamination. MDF is definitely the way to go for a box (if not using fiberglass)
Actually shipping a box isn't as bad as you might think. I ship several boxes a week through UPS.
I've shipped boxes from NY to CA and many places in between. Largest box I shipped was 48x20x20 and weighed over 100lbs and it only cost me $96 from NY to the midwest.
Also MDF or Birch ply are the materials of choice. Birch ply is about 2x as much as MDF (at least around here) but is also quite a bit lighter and much easier on your tools.