You can get oak veneer plywood along with many other veneers but if your
budget is limited, think of staining it so the tone is the same for the
different species used.

I bought some oak veneer plywood at the Borg but I discovered the "back" side
looked better than the featureless oak on the front. With a "natural" minwax
stain and poly my wife preferred the back to the front when choosing which side
should go out on a wall mounted secretary desk I was building for her. I
suspect that was garden variety birch or something.