/diy/ - Do It Yourself

I'm making wall cabinets out of plywood for my workshop. pic related is a model with heavily exaggerated thicknesses just to illustrate the construction. from what I've read this is the best way to make a cabinet.

I'll route channels to hold the top and bottom in place (the bottom is obviously my concern, don't want it falling out randomly). the rear rails will be pocket screwed into the sides (maybe also glued). obviously my model is missing the back, but it'll be 1/4 plywood or something. I will screw through the back, through the rails, into a stud. will this be sturdy enough to not fall off and kill me? they're going over my desk and will hold various equipment and tools, soldering stuff, all manner of /diy/ items plus books on the very top.

I want the top, bottom, and sides to be 3/4" plywood, but is this overkill? Could I get away with 1/2"? I want enough wood there for the channel to support the bottom wall.