What you have drawn there is a basic box type cabinet arrangement. I would lay out the three cabinets on some plain brown wrapping paper that comes on a roll. You can get that at any stationery section of drug stores or grocery stores.
Draw out the perimeter lines for the units. Draw the lines for what ever toe area/plinth type base you want. Draw in the thickness of the plywood you'll be using (I recommend 3/4").
For the overall height, you will have ends that are the height less the height of the toe area. The ends can be rabbeted at the top and bottom to accept the top piece and the bottom piece. I would recommend dadoes somewhere half way up for at least one fixed shelf (this maintains cabinet width).
The center section can be configured the same way. The center of the top and the bottom, make dadoes for the vertical divider. All the rest of the shelving can be installed on shelf clips with holes to provide up/down adjustment.
The back edges of the perimeter pieces for each cabinet can be rabbeted to fit a 1/4" plywood back. This will help square the cabinet. The backs don't have to be glued, but stapled into the rabbet. All the shelving gets cut short of the depth (figured to the back).
Face frames aren't necessary, but you could add them. If you don't, an iron on wood veneer tape can be used, or a solid wood edging to cover the front edges.