As peccavi says, in high school, I think I recall them saying before you graduate it should face as you describe, but after - the other way. (Sorta like switching the mortarboard tassel.) I may be wrong, or it might be BS someone told me that stuck with me. My thinking was, if someone asked to see it and you extended your hand, it would face the correct way for them.
I don’t believe I’ve ever owned a ring with a “correct” orientation. This is an interesting question. My initial thought is that I’d wear it upright for me (rat shitting on me.)
I had an interesting discussion about this topic with a friend recently. For some reason, I mentioned that I still have my Boy Scout ring from the 60s and that half the guys in my troop wore them oriented one way and half the other. (We all got them from our parents as a gift one year.) I was in the group that wore mine so I could view the ring correctly when I held my hand palm-down.
My friend quickly pointed out that one does not do that with tattoos. If you get a tattoo with words on your chest, you don’t orient them so you can read them when you look down. If you get “HATE” and “LOVE” on your fingers, you orient them so the guy you want to scare can read them…not you. (Who would argue with Mitchum or DeNiro?)
For those of you who may be wondering about Son_of_a_Rich’s joke:
The Phantom wears a ring that leaves, when smacking someone, the mark of a skull, right side up. So that’s how a ring is orientated.
i don’t see how anyone could argue with that authority! 
My wedding ring is a silver dragon clutching a jade chip. I’ve been told that I should wear it so that the dragon’s head is right-side up when I look at it, as opposed to right-side up to someone else looking at it. I tend to wear it in the former, but don’t always check when I put it on.
Yes. Facing me, I’m who I wear my rings for.
I made myself a set of corvid skull pewter rings - vaguely similar to the one below. But I wear them with the beaks facing towards me, over my knuckles.
I think it depends who the ring is for.
Well, if the goal is to scare other people, you are tattooed for them.
But when i wear jewelry it’s generally for me. I think I’d generally wear it so it looks right side up to me.
A tattoo on your chest is different, because there’s a natural “up”, and i would respect that. It’s my “up” after all, even if I’m looking down at my chest.
My wedding band has mountains carved on it. All the way around. So there is no ‘up’. It only comes off in surgery or an MRI. Shouldn’t matter since it’s gold, but I understand being careful.
One could argue that the fingertips are also a natural “up”.
Which way do you think is the natural up for fingers?
/* Manfully resists urge to demonstrate with crude gesture /*
I spend a lot of time with my fingers pointing down. Or out.
Quick: draw a picture of a hand. Are the fingers on the top or on the bottom?
Neither, they are to the side. But i guess I’m unusual in thinking of the hand that way.