Is half-inch plywood enough for shop cabinets, or should I use three-quarter?

If you’re buying material and want the stand to stay useful for heavier tools later, I’d go with three-quarter for the carcass. It adds weight and cost, but gives you more solid edges for fastening and more room to change what the stand is used for. Half-inch can still make sense for drawer boxes.

For a well-braced cabinet holding a modest load, half-inch plywood can work. A vertical divider and shelves tied into the sides help keep the box from racking, so the whole design matters more than thickness alone. I’d be more cautious with long, unsupported shelves or a stand that might eventually carry a heavy machine.

I’d choose thickness by where the stress lands. Three-quarter is handy where drawer slides or hardware need a firm fastening surface, and for shelves with a longer span. Half-inch is a reasonable option for lighter panels, especially with solid joinery and internal support. If you go thinner, make sure the top and base are doing their share of keeping the case square.