This weekend my dad is helping me do the wood cutting. I'm going with a product called Sandiply (from Home Depot) - it's plywood, very flat, and sanded smooth on one side. I just don't want the hassles of MDF dust and weight and am willing to put in the time to prepare the wood so the final cabinet looks good. It costs about $7 more per sheet than MDF, but I think the smooth side combined with the lack of warp (common in plain plywood) will make it worthwhile.
I'll be posting pictures of the progress next week - including layout and cutting of the wood. I'll be doing this on the byoac.com website under the 'Project Announcements' section. Do a search for "Saucer Invasion" to find it.