The walls are paneled with 4' x 8' x 1/4" birch plywood.
Above that is a 1" x 6" pine board -- the 1/4" birch overlaps it by about 2 inches.
Immediately above the pine is a half of a 4' x 8' x 1/8" birch plywood panel (ripped lengthwise). When this is done on both sides, the remaining space in the center is 4' wide -- perfect for a whole 4' x 8' x 1/8" birch panel (added after photo taken!). No waste and very little cutting.
Oak trim strips cover the lengthwise junctions between the panels. We used almond-colored panel moulding to join the "short" joints.
The supports are to allow the glue between the paneling and trim to set without gaps forming.