I have made lots of cabinets and use plywood veneer for the box and shelves. Mainly, oak, birch, maple, or cherry with oak and birch being the cheapest. Plywood interior made out of pine or fir is ugly and don't finish well. All doors, drawer fronts, and face frames are made out of solid wood.

I'd do more inquiry into this choice. The boxes should be plywood. If the question is whether the exposed surfaces inside the box should be raw plywood or a veneer over plywood, then I would choose the veneer. But make sure you understand exactly what the choices are. I am suspicious that the ''veneer-type material'' choice actually means something else, like veneered MDF.

I would get it specified in writing exactly how the cabinets are to be constructed. What thickness plywood for the boxes. Interior finish. Exterior finish. Drawer construction and materials. Door construction and materials. Brand, model, features for slides, hinges, latches. Size and eveness of gaps for inset doors. Overlap for overlay doors.

There was a thread recently by someone who was unhappy with his somewhat expensive custom cabinets. Various details were wrong - exposed plywood edge on drawer boxes and overlay doors that left too much space between adjacent doors, etc. He had not specified any of these details, indeed hadn't thought of them, beforehand. So, there wasn't anything to do.

If you are going to care about the details of your cabinets when they are done, then go read or at least skim a book on cabinet making, get educated on the options, and get the specifications in writing. So that when your builder installs MDF boxes instead of 3/4'' ply boxes, because they are cheaper for him and most buyers never notice, you can detect it and force him to tear them all out and do it over.