Still, as you mention, it seems logical that Sauron would seek out people who were in positions of power. My guess is that the Nine were mostly minor lords, who became kings after getting the rings. The Witch-King was probably one of the sorcerors, since he seems to be more powerful than the other Nazgul.
Also, what happened to the 3 elven kings and 7 dwarven lords who received rings ? What, if anything, did they turn into, and why not into Nazgul?
The three Elven Rings were never touched by Sauron (made solely by Celebrimbor) and so they weren’t corrupt from the beginning. As soon as Sauron put on The One Ring, Celebrimbor was aware of his treachery and hid the Three. They were never worn or used until after Sauron was overthrown.
IIRC, the Dwarves were simply too stubborn to be corrupted even by the Rings. They increased the greed of the wearers (not a difficult trick with the Dwarves) but Sauron could never really control control them.
Eventually, dragons destroyed several of the Dwarves’ rings, which were apparently not as difficult to destroy as the One Ring, and Sauron recaptured the rest.
One Ring went to Galadriel (sp?), who used it to preserve her forest. One Ring went to the caretaker of the Grey Havens (whose name escapes me), who, in turn, gave it to Gandalf when he arrived in Middle Earth, and the final Ring went to Elrond.
Just to expand on this, Nenya, the White Ring, went to Galadriel. Narya, the Red Ring, went to Cirdan (the caretaker you mentioned) who gave it to Gandalf, and Vilya, the Blue Ring, was given to Gil-Galad who passed it to Elrond before his death.
And to offer some more details around jsc1953’s comment:
It seems to me that he would seek out people who almost had power and were willing to do unfortunate things to get it…
nitpick encore. Narya and Vilya went to Ereinion (Gil-Galad). He surrended them to Cirdan and Elrond prior to setting out on the Last Alliance.
Of course the Encylopedia of Arda disagrees with me which is why I’m waiting for QtM. 
I assume you mean “when Sauron was overthrown the first time”. The elf lords used their rings between the end of the Second Age, when Sauron lost the One; and the end of the Third Age, when the One was destroyed (and the Three lost their power).
Checking in to say it’s good to see LOTR threads again here in the old Cafe. Just because we’re looking forward to Spiderman 2 doesn’t mean we’re any less ready to geek out over Middle Earth.
Internet access restored, truck driver chastised.
FAQ of the Rings explains much.
Keep in mind that the 7 and the 9 were first intended by Sauron to be kept by the elves; thru them he hoped to dominate the elves. But after he was discovered to be treacherous, Sauron seized them and handed them out himself to men and dwarves (with one possible exception for the dwarves).
Otherwise it’s been covered fairly well. Khamul, the easterner had one ring. The Witch King of Angmar had another, but little to nothing is said about his background. And the implication from JRRT’s copious (and sometimes self-contradictory notes) was that there were at least two, and possibly more Black Numenorean holders of rings.
BTW, here’s who had the 3 elven rings when. elven ring bearers
To elaborate on who had which elven ring when:
Celebrimbor gave Nenya the White to Galadriel. At that time, she counselled him that the other two should be sent away. So Celebrimbor sent Vilya the Blue and Narya the Red to Gil-Galad. This figures. Gil-Galad was of the line of Finwë and the high king of the Noldor.
Gil-Galad eventually gave Narya to Cirdan, but it is uncertain when. Possibly right away, possibly 1700 years later, when Gil-Galad marched away to Mordor. But Cirdan never wielded it, and gave it to Gandalf when he showed up in the 3rd age.
Gil-Galad gave Elrond Vilya the Blue “before he died”.
How likely is it that any of the Numenoreans (pre-fall) had rings? Sauron was playing Mr. Nice, trying to subtly manipulate them into attacking Valinor in a panic over death. He wouldn’t have given them rings (would have undercut the spur to attacking Valinor by providing what they wanted–immortality). Then, every bad Numenorean who went along on that little junket was destroyed. (Seems more likely to me that the barrow-down culture got 'em.)
Could Sauron have re-issued the rings, banking multiple wraiths per ring?
(The only note I have to add to the king debate is that the witch-king had a circlet/crown where his head should have been–doesn’t say when he got it though.)
Like, say, assistant managers.
All of the King’s Men didn’t die in Calacirya. There were Black Numenorean colonies back on the main continent of Middle-Earth, and a goodly number of the bad guys who didn’t go with the Great Armament and managed to not be on the island when it went ker-plunk were washed ashore around those colonies as well.
I’m hardly a Tolkien scholar, but isn’t there something in there about how a dragon’s fire could have melted the One Ring, except all the dragons are dead now? Maybe during the Council of Elrond?
Nope. It is stated that not even the fire of the greatest dragon, Ancalagon the Black who did battle with and was slain by Earendil, would have been hot enough to destroy the One Ring.