you can use my table saw if you want, I wouldn't trust the depot to cut what you want- they won't be very accurate (and have signs saying they won't be).
If you buy your sheathing material (say baltic birch ply or some hardwood faced ply) at woodworker's source (tempe location on kyrene-ish and eliot I think) I believe that they will cut it to what you want, and they will do a good job of it.
The way I would countersink the magnets in would be to use a forstner bit- it's designed to make flat bottomed holes for cabinetry work.
also, depending on the squareness of your 2x4 stand, you may have to do a lot of shimming of whatever panel work you put on. I'm not saying anything about your carpentry skills (although that could factor in too ;-)), I'm saying that 2x4 lumber is by no means consistent in any way.