MDF - Medium Density Fiberboard. I would get the 3/4" of 5/8" thick stuff. 1/2" might be alright bu the thicker the better. You want to use glue and screws on every seam and then caulk/glue all the corners from the inside to make sure their is no air leaks.

air space is best estimated using a calculator and some simple math and by deviding the volume into simpler shapes like rectangles and triangles. If you wanna get really accurate, use sand and add .25 or .5 cubic feet at a time until you fill the box, but usually that kind of precision not needed...