Hi John
If it were me, I would use 18mm cherry-flavoured MDF for the carcases, 6mm cherry ply for the backs, solid cherry for the face-frames, doors, door panels and top, and 12mm cherry ply, with the front edge lipped to 20mm, for the shelves. You will find that MDF does not take very much weight before it starts to sag, whereas 12mm ply is really quite stiff, especially if lipped front and back.
HTH
Steve