<In-Universe Chronology (as of October 2017)>
partly sourced from: https://www.torforgeblog.com/2017/12/20/where-to-start-with-the-dune-universe/
(Frank Herbert = F.H.; Brian Herbert = B.H.; Kevin J. Anderson = K.J.A.)

"The Butlerian Jihad"
Legends of Dune: Hunting Harkonnens (Short-Story) by B.H. & K.J.A
Legends of Dune: The Butlerian Jihad by B.H. & K.J.A
Legends of Dune: Whipping Mek (Short-Story) by B.H. & K.J.A
Legends of Dune: The Machine Crusade by B.H. & K.J.A
Legends of Dune: The Faces of a Martyr (Short-Story) by B.H. & K.J.A
Legends of Dune: The Battle of Corrin by B.H. & K.J.A
Great Schools of Dune: Sisterhood of Dune by B.H. & K.J.A
Great Schools of Dune: Mentats of Dune by B.H. & K.J.A
Great Schools of Dune: Red Plague (Short-Story) by B.H. & K.J.A
Great Schools of Dune: Navigators of Dune by B.H. & K.J.A

"The Corrino-led Imperium:"
Prelude to Dune: House Atreides by B.H. & K.J.A
Prelude to Dune: House Harkonnen by B.H. & K.J.A
Prelude to Dune: House Corrino by B.H. & K.J.A
Heroes of Dune: Paul of Dune (parts II, IV, VI) by B.H. & K.J.A
Wedding Silk (Short-Story, in "Tales of Dune") by B.H. & K.J.A
Heroes of Dune: The Winds of Dune (Part II) by B.H. & K.J.A

"The rise of the Atreides"
Original series: Dune by F.H.
A Whisper of Caladan Seas (Short-Story, in the companion book "The Road to Dune") by B.H. & K.J.A
The Waters of Kanly (story, Infinite Stars) by B.H. & K.J.A
Heroes of Dune: Paul of Dune by B.H. & K.J.A
Heroes of Dune: The Winds of Dune (part IV) by B.H. & K.J.A
The Road to Dune (Short-Story, in "Eye") by F.H.
Original series: Dune Messiah by F.H.
Heroes of Dune: The Winds of Dune (parts I, III, V) by B.H. & K.J.A
Original series: Children of Dune by F.H.

"The reign the God Emperor"
Original series: God Emperor of Dune by F.H.

"The return from the Scattering"
Original series: Heretics of Dune by F.H.
Sea Child (Short-Story, in "Tales of Dune") by B.H. & K.J.A
Original series: Chapterhouse: Dune by F.H.
Dune Chronicles - Hunters of Dune by B.H. & K.J.A
Treasure in the Sand (Short-Story, in "Tales of Dune") by B.H. & K.J.A
Dune Chronicles - Sandworms of Dune by B.H. & K.J.A

<Publication order>

1965 Dune by F.H.
1969 Dune Messiah by F.H.
1976 Children of Dune by F.H.
1981 God Emperor of Dune by F.H.
1984 Heretics of Dune by F.H.
1985 Chapterhouse: Dune by F.H.

1985 Eye by F.H.
1999 House Atreides by B.H. & K.J.A
2000 House Harkonnen by B.H. & K.J.A
2001 House Corrino by B.H. & K.J.A
2002 Hunting Harkonnens (Short-Story) by B.H. & K.J.A
2002 The Butlerian Jihad by B.H. & K.J.A
2003 Whipping Mek (Short-Story) by B.H. & K.J.A
2003 The Machine Crusade by B.H. & K.J.A
2004 The Faces of a Martyr (Short-Story) by B.H. & K.J.A
2004 The Battle of Corrin by B.H. & K.J.A
2006 Hunters of Dune by B.H. & K.J.A
2007 Sandworms of Dune by B.H. & K.J.A
2008 Paul of Dune by B.H. & K.J.A
2009 The Winds of Dune by B.H. & K.J.A
2011 Tales of Dune by B.H. & K.J.A
2012 Sisterhood of Dune by B.H. & K.J.A
2014 Mentats of Dune by B.H. & K.J.A
2016 Red Plague (Short-Story) by B.H. & K.J.A
2016 Navigators of Dune by B.H. & K.J.A

Extras:

1999 CliffsNotes on Herbert's Dune & Other Works by L. David Allen
2004 Dreamer of Dune- The Biography of Frank Herbert by B.H.
2005 The Road to Dune (Companion Book) by F.H., B.H. & K.J.A

<Reading order>

Any order would please Shai-Hulud