My rings in my inventory are arranged according to when I got them, so pretty much I could remember what rings comes first.
For the quest-obtained:
I got Bump ring from Remo, then Wish from Bill, then Defib from Katsumi, Divinity from Kin (which then dropped after I grabbed it, in Zen Gardens ^^ wink , Iron Will from Logan (I believe healers need Willpower... a lot of those) and finally Dervish from Agent, which I didn't use much because zOMG! shut down...
Rings that dropped twice or more: Taunt ^^;, Diagnose, Divinity (got 4 of these, but I salvaged the second), Adrenaline (the first one completes my Medic Set, pretty much my only completed ringset, I think... Oh there's Spacetrooper and Shaman in my ringset too) and Hack...