This post is not about the Frank Herbert Dune family (sorry Geoff), but the various surviving Greek tragedies by Aeschylus, Sophocles and Euripides which tell the story of the descendants of King Atreus of Mycenae. All these three Tragedians told various episodes of the story, which also interlace with Homer’s Iliad.
They can be read in the order they were written (chronologically) as I did, or within each playwright’s oeuvre. But if someone wanted to use them to read the history of the family in order (for those budding directors looking for a replacement for the Game of Thrones saga perhaps), it would look something like this, with inconsistencies within according to the author and the emphasis of the play. The way some characters such as Odysseus and Menelaus, Clytemnestra and Electra are portrayed is interesting to compare.
Iphigenia in Aulis (Euripides)
The Iliad (Homer)
The Women of Troy (Euripides)
The Libation Bearers (Choephori) (Aeschylus) or Electra (Sophocles)
The Furies (Eumenides) (Aeschylus)
Iphigenia in Tauris (Euripides)
Because Agamemnon and Menelaus came to their thrones via their father Atreus, who had previously ascended to the throne of Mycenae when King Eurystheus died fighting the Heracelidae, so the various Heracles plays could precede this series. Other sequels shooting off from The Iliad include the tales of Odysseus, told in Cyclops (Euripides) and The Odyssey (Homer), and the fate of Ajax in Sophocles’ Ajax.