For my personal experience, I have learned that the looser the ring fits on your finger (without falling off) the better. This way you can easily remove it when you need to use it to perform. Also the thickness depends on personal preference. Me personally, i prefer a thicker ring made of tungsten carbide (I have dropped it on concrete more times than I can count and it still looks great!). It makes it easier for me to perform ring/gryphon rolls and is more visual for moves like ring thing, circuit, etc. In fact I combine it with my "Ninja Rings" routine using a fun gimmick called "Ninja Plus" by Matthew Garrett.
Here is a video or two of me performing some ring magic
Hope any of this helps!