Orius
Unrepentant DM Supremacist
It's not that it's unique, per se, it's that it was the first.
The various settings it seems like? They were ripping off it, not the other way around.
Greyhawk suffers from the fact that it's been poorly marketed for 30+ years. It was always so intrinsically tied to Gary Gygax that once he was out at TSR, Greyhawk was never a priority for them, and it showed.
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Greyhawk isn't an influential or major setting because it's unique, it's because it's the seed that so many other things in D&D sprouted out of, that it has a special and unique place in D&D history and lore.
Greyhawk suffers from what TVTropes calls Seinfeld is Unfunny, because it established a lot of groundwork in what is a typical D&D setting, it doesn't seem all that original even though it was in fact one of the first. And the Realms eventually eclipsed it in popularity. That's why a compelling setting hook is hard to come by, because often the other settings define themselves by what sets them apart from "normal " D&D, i.e. Greyhawk.
Default setting? Huge overlap with the Realms.
Domain management? Overlaps with Birthright.
Recovering from a recent major war? Overlaps with Eberron, and the old guard has a lot of haters of the Greyhawk Wars.
The old guard appreciates that it it's a relatively loose setting that a DM can make his own, but those guys have all made their own unique Greyhawks. That's why they're so invested in it, and they enjoy sharing stories about what they did with it, but that makes it harder to commercialize the setting, and was probably a big obstacle for Sargent's material.
It's a good setting and it's historically important to the game, but there's the issues of making newcomers get interested in a vanilla setting which was influenced by earlier fantasy tropes than what's familiar to them in a world where D&D has been shaping said tropes for over 45 years.
In my view the single best of REH's Conan stories is The Tower of the Elephant. Other classics are The Phoenix on the Sword, The God in the Bowl, The People of the Black Circle, Black Colossus and The Scarlet Citadel. Queen of the Black Coast is well-regarded but you have to do more work to ignore the racism. I prefer Xuthal of the Dark to Red Nails but that's probably a minority opinion. I'm not a big fan of Beyond the Black River but many regard it as a classic. The Hour of the Dragon is longer but fun. I think most of these, maybe all, are available online via Project Gutenberg Australia.
That's a pretty good selection, but the The Scarlet Citadel has a lot in common with The Hour of the Dragon, and Dragon is a far better story. Black Colossus isn't bad but I'd put in second tier as well. Rogues in the House is also another of the top Conan stories, and belongs on that list.
The Phoenix on the Sword was the first published, and it's a good starting point because it introduces the character and the setting. Chronologically, it's the third last story though. REH didn't write the stories in chronological order, so there's no more than a loose chronology among them. Generally, the earliest stories have Conan as a thief in his late teens, and in the three final stories he's a king. In between, he's a soldier, mercenary, pirate, or raider depending on the story, and nearly all the weak stories fall here, as they tended to be written for money. Reading them in publication order is fine. The more recent chronologies put The Frost Giant's Daughter/Gods of the North at the very beginning.
The Tower of the Elephant, The God in the Bowl, and Rogues in the House are part of the thief phase. Rogues is probably the last of the stories, while there's some dispute as to which of the other two come first.
Red Nails is often considered one of the best, but I didn't like it that much. It's one of the bleakest of the stories, and it has a lot in common with Xuthal of the Dusk which I'd read first. Queen of the Black Coast is very good, and while it's very easy to find racist elements in it if you go looking for it, it has a Conan who's matured past his thief days and has an evolving world view on the gods and religious views of the Hyborian world. Beyond the Black River is pretty good. On the surface it comes off as little more than a settlers vs. Indians story from colonial America. But Conan blames the situation on the social inequalities of Aquilonian feudalism, and feels if the barons shared their land more equally, there wouldn't be population pressures encouraging people to settle in Pictish or Cimmerian lands where they get slaughtered by angry natives. And the Picts themselves are nastily violent xenophobes.
The Phoenix on the Sword, The Scarlet Citadel, and Hour of the Dragon are chronologically the final three stories, in that order.