I would guess Renegades. That's what follows directly after White Dragon, but if you want to add that set on as "original" than you need to go all the way through to All The Weyrs of Pern.
The first three have been sold as a trilogy, boxed together in a slip case. I have it on my Anne McCaffrey book shelf. I wouldn't have thought of Renegades of Pern as a fourth in that set. If anything, I think my vote for a fourth would be Masterharper of Pern.
You may be right. In fact, the whole homosexual thing didn't have any reason for being in the story line. During the period covered by the first three books (I think it was in The White Dragon) she had a girl -- Mirrim -- become a rider of a green dragon. And in later books we learn that female dragonriders (other than queen riders) were the norm in the early days of the colonization of the planet, centuries (millennia) before the time of the first three books in the series. So there was no need or reason to have ever made that even a side issue in the series.
That said, none of Anne's books were in your face about it. It was just there, in the background. Todd made it a central plot element, even though doing so was totally unnecessary. I guess he's still writing more Pern books and continuing to cash in on his mother's legacy, but I won't buy another of his books. I'm done.
I like reading the books in order of how they relate to the timeline of Pern (start with Dragonsdawn and then go up through the history) and some of the books overlap, but from after the first three that were published, it's Renegades, then Dolphins and then All The Weyrs. Masterharper is set before Dragonsflight, and I always see that as a stand alone. Plus, you add in the Dragonsong triology which falls somewhere in the middle of Dragonquest. Those are the set that covers the larger portion of Pernese history and the "modern" Pern.
I actually haven't read the solo stuff by Todd. The only joint book I've read is Dragonkin. I have the second two of his trilogy, but I couldn't find the first and I don't have the sequals to Dragonkin (the perils of shopping at the used bookstore)
I've just reread all the Pern books, except Moreta and Nerilka (in fact, I'm almost done with Dragonkin, which is the end of the road until I can get ahold of the others :( ) and it seems to me that Anne pushed the overall sexual politics of Pern as much as she could, given when the books were being published, and that the Werys were the place that she could explore that theme. I disagree with you. I think she would have had much more involving gay riders and that it could have even been central to other stories and the overall politics of the world. There is a very real progression in the publication order of how she deals with sex in her books. She really glosses over stuff in the first two, gets a little more obvious in White Dragon, and by the late 90's, she's got things right out in the open. I'm not just talking about homosexuality, but also woman's sexuality, with woman in the Werys and some in the crafts being much more sexually free with their favors and woman in the holds being pushed into childbearing.
Sexual politics and population control is a big issue on Pern, especially with all the plagues she writes in (she really has a thing for Plague)
The reason greens stopped having female riders was because of Plague dropping population and holders trying to increase population for land rights. Woman were discouraged from going to the Weyrs (in fact, Dragonseye makes it a central storyline) and overtime it was forgotten that woman had even been riders on the fighting dragons.
I don't know how the Todd books are, in terms of quality, but I'm going to bet that the sexuality he has in them is not anything she would disagree with. Plus, most of those books were written before she died. She may not have written them, but I wouldn't be surprised if she had read them and okayed them.