There’s a complete list of Mum’s works at her website, annemccaffrey.net under Books -> Bibliography. Under Books -> Series, you can pick the Dragonriders of Pern and get just the Pern books.
Chronologically, the current order would be:
In the first Pass:
The Chronicles of Pern: First Fall
In the Second Pass:
In the Third Pass:
Dragonrider (tentative title)
In the Sixth Pass:
Moreta: Dragonlady of Pern
In the Ninth Pass:
Dragonsinger (overlaps with Dragonquest)
The White Dragon
Dragondrums (overlaps with The White Dragon)
Masterharper of Pern (overlaps with all of the above and more)
Renegades of Pern
The Girl Who Heard Dragons (anthology)
All The Weyrs of Pern
The Dolphins of Pern
The Skies of Pern
Also note that the three-book omnibus, “The Dragonriders of Pern” encompasses Dragonflight, Dragonquest, and The White Dragon.
“A Gift of Dragons” is a collection of short stories which are mostly set in the Ninth Pass.
There are also some other short stories published in various places.