Bary,
Not too sure about gyroscopes, but as I remember from the toy one I had as a kid and what I've seen on science shows on tv, the key is balance, as would be the case on any spinning wheel. I would say that brass would make a fine scope. Turning this on a lathe?? If I was to make one, just sitting here brainstorming, I would make the frame from steel (Stainless;)??) and the wheel or "rotor" from brass. Brass seem to have built in lubricating qualities. Just an opinion. Use at your own risk. Sounds like a fun project though :)