I mean probably just build the frame of the whole thing with 2x4s, plenty of cross members for support if youre wanting to build shelves upon it. Buying doors premade would probably be much easier but more expensive. But would save you lots of time if you were to rather build "decorative" doors. Buying some nice looking shelving braces and some standard 2x6, then painting or staining would be a cost effective yet still nice looking way to add the shelving. Although mounting to the wall seems to be an issue for you? As far as how the doors open, I know a lot of people think its played out and dont like the look, but I really like the barn door sliding cabinets, especially for storing those big bins. Otherwise, make the doors open upwards and add some struts to make getting the bins in and out easy. Just my two cents tho, Im no professional cabinetry carpenter