I did the bottom of a Satan's Hollow cabinet a while back (different shape but built by to the same basic design).
I just use any wood available, which usually means 3/4" plywood mounted to scrap 2x4's on the sides, front and back panels. The 2x4s are overkill, but I tend to have those laying around more often than I do the furring strips I use when I scratchbuild a cabinet (buy those if you don't have a scrap 2x4 to use).
Then put some feet on the new cabinet and jack them up at least an inch. Better yet, install a 2x4 on each side and then put the feet into those and you will never need to fix the bottom of the cabinet again.