Plywood doors for kitchen cabinets is very common.
As for as the thickness of the plywood goes, you first need to choose a door style. A solid one piece panel or a frame and panel construction. The thickness for the one piece will be 3/4” but the panel for frame and panel can be only 1/4”.
MDF is now commonly used for paint grade cabinet doors and drawers. The MDF does not have plys like the Plywood and the edges can be routed.
If you don't have time to do it right the first time, when will you have time to do it over?