Plates need only to be thick enough to be rigid enough to maintain accurate plate spacing. If using a multi plate design the spacing should be exactly the same everywhere [the recomended is 1/8th inch or 3.2 mm]
As the surface of the plates is where all the work is done the surface area is the most important.
If using brute force electrolysis then a highly conductive electrolyte is used. I imagine that provided the supply / cell interconnecting tubes are long enough then the resistance would be great enough that current flow would be reduced but they may need to be several metres long.