Reading around, Im guessing you should do a mix of both. It will save you money from all 3/4, but cost you a little more if you were to use 5/8. I think that because most people use 3/4, others follow in their tracks to assure that their cabinet is okay, where realistically, 5/8 should do the job the same. I figure that if you use 3/4 on the places it needs the most, then you should be good. For example:
BASE = 3/4
LOWER = 3/4
UPPER = 5/8
MONITOR = 3/4 reinforced
PANEL = either depending on plexiglass and router bits available.
The only thing I would say NEEDS to be 3/4 is the base, if you design the cabinet right. Put a few small studs in the base, attach some casters, and youre fine. Just make sure you use some small studs on the inside for screws to catch. Better safe than sorry right?