If the GtGs guys get the three, perhaps I have a shot at one of the others. Would I rather become a wraith or be driven mad with greed?
The seven don't *necessarilly* drive you mad. I'd say that, all told, they're the better choice.
The seven and the nine were, more or less, the same. It was the nature of the dwarves themselves, that kept them from being dominated.
I decided to split this thread because it was straying far afield from the original topic topic (yet onto a topic that I love :) ), and also because I am going mad with thread-splitting power.
@Greywind
I would contend that the Seven and the Nine were distinct in their powers and effects, each granting power according to the nature of the races for whom they were forged. It seems clear, for example, that the Nine granted invisibility, while the Seven did not.
Indeed, the Three, The Seven, and The Nine all appear to magnify the innate abilities of their respective races, and grant additional abilities that allow the bearer to achieve goals commonly desired by that race; i.e., The Three allow the bearer to preserve a semblance of the Elder Days, The Seven assist the bearer in amassing mineral wealth, and The Nine grant the power to command and gain dominion over other Men. It is my belief that these were the original powers of the Rings, as imagined by Celembrimbor. The fact that The Seven and The Nine also had a darker side was due to the influene of Anatar in their creation; the fact that that darker side was not nearly so effective corrupting Dwarves as Men is, as you said, due to the nature of the Dwarves themselves, who were created by Aulë specifically to resist dominion by Morgoth (and associated dark powers).
Anyhow, those are my thoughts on the matter :)
I'd rather have these 7-9 rings (the picture shows 8, omitting White, and you could also leave out Black very logically).
I think that most of y'all would enjoy listening to The Tolkein Professor, if you don't already. Consider yourselves so advised.
I think Paul could be The Tolkein Professor… 
@jffdougan
Wow! I now know what I'm doing on the plane to and from conventions this year!
The Three were untouched by the Darkness, having been forged solely by Celebrimbor.
There is also some question about the 7 and 9 being the "16 lesser rings of power."
@ Envisioner, I have no love for the Rainbow Lantern Corp. 
Yeah, Sauron wasn't able to get his hands on the Three, so they remained "pure", but had he ever got hold of the One, he'd've been able to corrupt the Three as well. The Seven couldn't be twisted into making the Dwarves properly corrupt/enslaved like the Nine were for Men, so they instead amplified the Dwarves' natural tendency toward "Ooh, shiny!" and this is what caused Thror (father of Thrain, father of Thorin) to go a bit nuts with his whole obsession-over-hoarding-treasure thing, resulting in Smaug going "Ooh, many shinies in one place...yoink!".
I like the online Encyclopaedia of Arda for all my Middle Earth factfinding needs (didn't use it to type the above - did that from memory as I only reread the books a year or two ago :)). You can look up anything and there'll be a nice article on it, with references and links to related topics and everything :).
My suggestions in working through his stuff:
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Start with his Hobbit essays. They form the basis of the book he published last year.
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Then do the Tolkein and Faerie & Fantasy courses, in whichever order you like
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Listen to the old Riddles in the Dark stuff last, aside from the first episode or two where he and Dave Kale explain the project goals. It's very specific to thinking about the Hobbit film adaptations and predicting, so some of those are now outdated.
I've never understood the numbers. 1, 3, 7 and 9? Why not 5? Why no even numbers? Why did the elves get fewer rings even though they live longer?
The elves got the fewest number I think because they are the hardest to tempt. Men got 9 because the race of men craved power and were therefore easy to manipulate and turn to the darkside.
Well why only nine? If all Sauron had to do to corrupt men was to give them rings, why not manufacture several hundred rings and have an entire army of Nazgul at his command?
I'm guessing there's a lore or mythic component to the numbers. Tokien tried very hard to make names in his story invoke a feeling of old Arthurian legends. Also, high quality rings are not easy to make, especially with pre Industrial Revolution technology. I imagine he gave up whatever his social life was to make 19 of those things in such a short amount of time. It's 20 if you count the One Ring.
That's a shame. Blackest Night was an incredible story, and was much better quality than the current Green Lantern comics. Ever since that "War of the Green Lanterns" arc it's all gone downhill…
So the other rings actually provided some mythical such-and-such? That's news to me! I've only seen the flicks, as I stopped reading Fellowship in grade school after Tom Bombadil bored me to tears.
Honestly, outside of the Ring Wraiths, the other rings don't affect the plot of the books that much. At least from what I remember.
They are part and parcel to a lot of character motives
Yeah, the Hobbit would never have happened (retrospectively, after LotR was written) if the Dwarves had never had their rings - as I mentioned above, it was Thror's ring which caused him to become overly obsessive with his treasure, hoarding it and providing an irresistable pile of loot for Smaug to fly in and sit on top of. Fortunately a chance meeting in a pub over by the Shire set of a chain of events which ultimately prevented victory for the bad guys (since with Smaug dead, Sauron couldn't recruit him to kick arse in the north during the War of the Ring, meaning that the Men and Dwarves of Esgaroth, Erebor, and the Iron Hills were able to band together and defeat the armies invading from that direction while Aragorn was distracting the Mordor forces over by the Black Gate to give Frodo time to destroy the Ring). I don't recall whether any of the other Dwarven rings had any effect on any other creatures - I think a few were taken by dragons or otherwise lost, but I think Sauron got his hands on a couple of them, one of which may have been Thror's but I can't remember now.
The Elven rings are definitely important, considering they're all possessed by important characters - if I remember rightly, Gandalf has Narya (which has fiery powers and thus boost his already epic powers since they're fire-based). Galadriel has Nenya, which I think is what gives her the power she has to keep Lothlorien in its undying, "outside of time" state with all its lovely trees and stuff - after she goes into the West, I think the wood sort of goes "back to normal". I can't remember the name of the third ring but it's worn by someone else important - Celeborn or Elrond or one of those. Plus as mentioned, though Sauron wasn't able to get his hands on the Three to corrupt them during their creation, had he ever managed to regain the One, he'd've been able to do so then, thus breaking the power of Galadriel and the others, corrupting them or whatever. Thus providing another reason to need to destroy the One - apart from the fact that Sauron's regaining it would return him to full strength, it would give him power over those who formerly stood against him most strongly.
In a way, this means that the Nine have less effect, in a way. Yeah, they made the nine Men corrupt, turning them into Wraiths of the shadow world who follow Sauron's orders, emit fear wherever they go, command his armies on his behalf, and kick arse in combat, but all those things are more…immediate. The slow damage inflicted on the Dwarves and the potential corruption (or whatever would happen) of the Elves (and Gandalf?) are much more long-term. Even with the Witch King, Lord of the Nazgul, destroyed at the battle of the Pelennor Fields, Sauron's still nowhere near losing the war as a whole. It just seems like the Nine are more of a problem because the main characters, in particular the one who is writing the majority of the book (LotR is mostly written by Frodo except for the end part which is written by Sam, whereas the Hobbit is written by Bilbo, who's also responsible for the intro, "Concerning Hobbits", of LotR), because they're actively out to physically get hold of/kill him so they're more of an immediate threat.
It's because Tolkein was a very devote Catholic. These numbers are important in biblical numerology. One is for God. Three represents the Trinity. Seven is the number of perfection and the sabbath. Nine is 3x3 so basically three trinities. In my experience if you have a question about why Tolkein wrote look to three places: Catholicism, older myths and legends (mostly fairy stories), and anti-war sentiment from his time in WW1.