The base needs to support the entire weight of the cabinet, as well as all the equipment housed within. It will distribute the weight across the four casters, which will be attached in a later step.  I used a 19" monitor, which is about 54 lbs. The monitor shelf needs to be sturdy enough to handle this weight. This shelf will also serve to keep the cabinet sides from bowing.

Start by cutting two 2x4s at 20 inches.  These are the front and back framing members.

Cut two more at 30-1/2".  These are the side members.  Finish with two at about 16".  These last two are the monitor supports.

Cut a piece of plywood 20 x 30-1/2".   Cut another at 20 x 18, which will be the monitor shelf.

Finally, cut a plywood strip 20" x 2". This will be the backing board mounted atop the shelf to keep the monitor from slipping backwards.

Sink one screw into each corner.  Then sit the ply base atop the frame to ensure it is square.  Then drive an extra screw into each corner of the frame.  Screw the ply top to the frame with a screw in each corner.  You can drive more but gravity, all the components, and the cabinet sides will keep it in place.

[Update- I found that if I laid the plywood base, good side down, on my table, I could align the 2x4s much easier atop them.  I made sure the everything was exactly lined up with the edge of the plywood, then screwed a 3" wood screw into each corner of the 2x4s to really secure it.  Then I finished securing it with 2" screws.]