Just a few suggestions to go along with all the info so far. When using a circular saw, the good face of what you're cutting should be down, for a clean cut to the face. Depending on the thickness of the plywood you're cutting, will determine the tooth count. If you're cutting 3/4" hardwood plywood, you will get an easier cut, but not necessarily as smooth with a tooth count less than 40T. A carbide tooth blade will give the best cut.
As for a straight edge, you could get by with something simple as a piece of 1/4" plywood or masonite. The thicker your straightedge is the more clearance you need for the motor to clear over it. It should be wide enough to get your clamps out of the way of the saw passing. The straightedge can actually be used on either side of the baseplate, but your measurements should be made to which side of the tooth you are cutting to.
For setting up under the ply, make sure both pieces have the same support, so when you cut, there is no "falling" of either piece. Something like 2 x 4's work pretty good. When setting the depth of the blade, the gullet (gap between the teeth) of the blade should be clear from the bottom, to allow debris clearance while cutting.
Once you start your cut, don't stop. IOW, make sure you are completely set up and ready to go. Make sure you have your cord/extension cord laid out safely from the cut, and you have enough cord to get the saw to go all the way. I know this sounds very elementary, but it can be an overlooked problem.
The HD's I've been to do a fair job on vertical cuts. For horizontal cuts, they push the material through the saw (made stationary), and use kerf keepers (blade thickness spacers) to position the top piece during and after the cut. The quality and accuracy of their cuts depend on who is on duty that day.