A metal backing provides screening, but a wood backing is convenient for temporary mounting of brackets to support controls, speakers, displays or other chassis-mount components.
Don't worry about the conductivity of a metal backing - just cover it with Fablon for added insulation. If you do go metal (or stick copper foil on plastic or wood), one terminal, marked 'Ground' should connect direct to it, and ideally, you should provide extra connection points to it just off the edge of the breadboard at either end of each bus strip so that you can get a better ground connection to it, but unless you use copper foil (or PCB) that you can solder individual wire sockets (salvaged from a turned pin DIL socket), into, that can be difficult to do.