From a thread on the American Heraldry Society forum, this post from Hassan Kamel-Kelisli-Morali gives the following information on what is customary to put on signet rings, the materials from which they are made, and on which finger(s) they are usually worn:

In the British Isles:
- Tend to favor the use of the crest, crest and motto, or badge.
- Tend to favor the use of solid gold signet rings (as opposed to a stone set ring).
- Tend to wear the ring on the small finger of the left hand.

In France:
- Tend to favor the use of the shield, with coronets of ranks when appropriate.
- Tend to favor the use of solid gold signet rings, for the most part. There are some cases of semi-precious and precious stones, engraved with the arms.
- Tend to wear the ring on the ring finger (sometimes the small finger) of the left hand.

In Germanic Countries:
- Tend to favor the use of the entire armorial achievement. However, there are cases where shield and coronet of rank, if appropriate have been used.
- Tend to favor the use of a gold ring set with an engraved semi-precious or precious stone.
- Tend to wear the ring on the ring finger of the left hand.

In Greece & Other South East European Countries:
- Tend to favor the use of solid gold rings (gold set with stone are somewhat common).
- Tend to wear the ring on the small finger of the right hand.

In the Iberian Peninsula:
- Tend to favor the use of both, solid gold and gold set with a stone.
- Tend to wear the ring on the small finger of the left hand.
Given you have a grant from Lyon (I assume, as you state from Edinburgh), I would go with the crest or crest and motto.