I've had a copy of a book titled The Dragonriders of Pern for years (the cover is falling off), and I read it once a year or so.  It was a Reader's Digest book way back in the 70s, which is when I found this copy, and apparently it contains three novels from the series, including The White Dragon.  I found The Renegades of Pern.  I'd like to read more of this series, but there are so-o-o-o many titles, I thought I'd ask if anyone can suggest an order for the books in this series?  Please PM.  And thank you.

I don't know if I'm an expert on McCaffrey, but I've read all the Pern books exceptthe recent ones that were written by her son, so I think I can comment on them at least. :)

Well, you started in by far the best place with the original trilogy in The Dragonriders of Pern omnibus (the titles are Dragonflight, Dragonquest, and The White Dragon). They were the first written and even though they're right in the middle going by internal series chronology they provide the best intro to the world of Pern. After that. . . there are several directions you can go, because the series is scattered across several thousand years and features a couple of distinct story arcs.

You can continue going forward chronologically from The White Dragon and read about the same characters you already know rediscovering their origins and technology, in which case you would read The Renegades of Pern (which you mentioned you already have), All the Weyrs of Pern, The Dolphins of Pern, and The Skies of Pern.

You can read a stand-alone trilogy focusing on the Harper Hall and taking place at the same time as the original trilogy: Dragonsong, Dragonsinger, and Dragondrums. This is a more YA-feeling trilogy, but is also a favorite of mine and many other McCaffrey fans.

You can go to the beginning and see the founding of Pern, in which case you would read Dragonsdawn, followed by The Chronicles of Pern: First Fall.

You can see what Pern was like in its sort of middle period, when the Passes were coming regularly and people had forgotten their technological background, in which case you would read Moreta: Dragonlady of Pern and Nerilka's Story. (This is one of my favorite sections, but is a bit of tear-jerker.)

Or you can read The Masterharper of Pern, which might be my favorite Pern novel, and which is a sort of prequel to the original trilogy; however, it benefits from you having read at least the Harper Hall trilogy as well first.

Finally, there is one completely stand-alone novel, Dragonseye, which takes place in the second Pass, so earlier than Moreta but after The Chronicles of Pern.

Gloria, Anne McCaffrey recommends that you read the Pern books in the order she wrote them, so you could just get them in order by original publication date. I'm sure they have a list in order for you somewhere on Wikipedia.

Posting a group "thank you" here.  Received great feedback on this question, very helpful and much appreciated.  i even got a great deal on a couple books to continue my Pern reading.  Everyone was so helpful.

http://www.librarything.com/series/Dragonriders%20of%20Pern:%20Publication%20Order

here is a link to the publication order of these books on librarything.com.  These lists are done by users of the site, but I have found ones I have used to be accurate.