The inside ring is made of stainless steel  for every ring. It needs to be this material for stability reasons, so the ring can`t get deformed. Deformation would lead to breaking of the inlay. The rings made with an inside ring of stainless steel are hardly to deform even with heavy hammering on them.

The outside ring can be made from various materials.
See below.
You can choose a metal for the outside ring.
16 ga is about the thickness of a penny. 18 ga is a bit thinner. For a good stone inlay thicker metal is better. If you have very thin items to embed 18 ga would be possible to make.

Options for the outside metal:

Copper 16 ga
soft, warm dark color, gets darker by the time
as it is used only for the outside ring, it will not stain your skin! But if you want a Copper ring for medical purpose, I can make a ring for you which has skin contact. Please write a message to me in this case.

Brass 16 ga
bright yellow-golden, hard alloy of Copper and Zinc

Bronze 16 ga
Alloy of Copper and Tin, in opposite to Copper/Zinc for Brass
softer than Brass and darker, between copper and gold

Welding steel 16 ga
blueish undertone

Rich low brass 16 ga
softer and a little bit more warmer yellow than normal Brass

Nugold 18 ga
Brass with a higher copper content, also called "Merlins Gold"
darker than yellow Brass