I was going to hold off asking rendering questions until I got the whole model built in rhino but I am far enough along to maybe ask some questions in this area.
In these pictures, the grid lines are—shall we say–not so good. I get the zipper pattern on the top rings and interference patter on the side rings.
On other systems I have had to adjust anti-aliasing settings to get those to come out right. What would I need to do in Rhino to fix those?
In the Render drop down menu open Render Properties to access the Anti-Aliasing sample setting. If the images you posted are the rendered display mode and not actual renderings, then the anti-aliasing is controlled by the graphics card. You can open Preferences (CMD + ,) in Rhino for Mac and go into the OpenGL section to adjust that.