I've tried wearing more than one ring on one hand and it doesn't look good. It's overkill, I think. So I think a ring on either hand. Nine times out of ten I'll go for pinky rings, but not always.
When I finished my residency in New Orleans, I went to L.A. where I would work as a doctor during the day, and then at night I would actually go to The Improv and do standup, all the while kind of cultivating my comedy resume.