Making your own wheels is probably not a great idea, since the best material is polyurethane rubber, which is a complete pain to turn. There are several sources for the noise. The first source are the actual bearings used. They need to be precision types, with shields on both sides (to avoid dust ingress). The second source are the actual wheels, or rather their contact with the wood. This is essentially the same noise you get when skating on a surface (at a speed of 20mph, a 70mm wheel does about 2270 rpm), but you are running on a comparably soft and probably bumpy surface, therefore generating noise. The third source of noise is when these contact vibrations are transmitted from the wheels into the arms and the frame, and the whole thing starts to vibrate.
So, in order to keep the noise down: use high quality shielded bearings, largest diameter wheels that will do the trick (although that limits the smallest diameter you can hold) and make sure the contact surface is as smooth (and hard) as possible.
I knew all of this before I even started the post. I was just wondering whether anybody had ever compared different materials for any of the parts. I suspect no, since none of us are in the business of building steady rests.
