Lines that are too fine will clash visually and technically. If the ring looks too blurry online, the real ring will also be a little blurry. If you are unsure, design the details so that they are too big rather than too small.
too fine
good
perfect
Design around the ring
Do you want to make your own design around the whole ring? Choose your width, the outer shape and the ring size. At the bottom right in the 2D view you can see the image ratio.