Eight

Hi there, I'm currently planning (and to an extent, building) a simple computer system based around a Z80 cpu. Initially, I plan to power everything from standard batteries and when finished, I hope to make a simple case for it. Most of the electronics side I know enough about but am a little lost on the question about grounding though. If the circuit board and components all link to a central grounding point - should I be connecting this to a metal frame? Or for devices powered by DC batteries, is it enough just to put in a plastic case? I know that metal frames/chassis/cases (whatever) help with interference etc. but aside from that, should I do it? I'm guessing things would be different if the device was connected to a mains power supply? I'd really appreciate it if someone could help me out on this - or point me in the right direction. I've searched the web but found nothing that has really clarified things to me. Thanks, E