Building with pre-veneered plywood is dicey. If you're really good you can do it, but your joints must all be mitered for square corners, and it's not easy to get it right, especially as the outer veneer layer tends to be very thin and easily chipped at the edges. One exception is real BB (not Chinese faux birch), which has an outer ply the same thickness as the inner plies. If you can find maple veneered plywood with a full 1mm or thicker maple layer that's a different story. Or you can use solid wood on the corners, but that also complicates the build.
If you want to veneer over plywood that's OK, but be sure the plywood doesn't have a deep grain, as that will show through the veneer. That rules out North American softwoods. BB is OK, as is Arauco (radiata pine). I don't care for MDF either, but it's probably the best substrate for veneer, having no grain.