I've read a handful of Conan books in random order without feeling like I'm missing anything, but I don't think that's really intended, particularly for the early books written by Robert E. Howard himself.
Several different authors have tried to put together a chronology, but according to Wikipedia : A completely consistent timeline that would accommodate every existing Conan story is impossible for several reasons.
These include: (a) errors that crept into the earliest chronologies (b) subsequent disregard by the early chronologists of chronological evidence in later-discovered Conan material contrary to the existing schemes (c) similar disregard for this contrary evidence in the writing of much post-Howard Conan material, and (d) disregard of both the existing chronologies and chronological information established in previous stories by Howard and others in the writing of other post-Howard Conan material.
The page I linked to has several of the major chronologies, so you could either pick one of those (I'm considering following the Robert Jordan version, since I'm a big fan of his), or you could look to see where they're similar and make your own.
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The Barbarian Keep by William Galen Gray looks like the most comprehensive timeline of Conan by Howard and others, but there is little in the canon that compels one to read in any given order.
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I have the conan stories by Howard in the Gollancz Fantasy masterworks series.
Its two books and claims the have all the conan stories by Howard in in-universe chronological order.
That does not seem to be the order in which they were written.
A nice series of stories.
The Conan Chronicles - Volume 1: The people of the Black Circle
The Conan Chrnicles - Volume 2:
The Hour of the Dragon
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The 12 book series published by Ace that attributes the authors as Howard, L. Sprague de Camp and Lin Carter is an excellent start.
The series includes stories by Howard that were published and unpublished, and the other two authors finished partially written manuscripts and outlines and ideas left by Howard.
Howard had a grand chronology in place from early on, including maps, but he did not publish the stories in chronological order.
The 12 books, in order, are:1 Conan (with a fabulous Frazetta cover)2 Conan of Cimmeria3
Conan
the Freebooter4 Conan
the Wanderer5
Conan
the Adventurer6 Conan
the Buccaneer7 Conan
the Warrior8 Conan
the
Usurper9
Conan
the Conquerer10 Conan the Avenger11 Conan of Aquilonia12 Conan of the Isles
As for other works I have not noticed that the authors totally respect the original Howard vision.
Perhaps some do.
I would not consider works outside of these 12 books to be canonical.
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Truly the stories are not meant to be read in order.
The stories were not published in a any particular order because REH meant for the reader to believe that the teller of the story, Conan, told the stories as he remembered them randomly.
Source:"As for Conan's eventual fate - frankly I can't predict it.
In writing these yarns I've always felt less as creating them than as if I were simply chronicling his adventures as he told them to me.
That's why they skip about so much, without following a regular order.
The average adventurer, telling tales of a wild life at random, seldom follows any ordered plan, but narrates episodes widely separated by space and years, as they occur to him."
Robert E. Howard, Letter to P.S. Miller, March 10, 1936.
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Is there a recommended order of reading for Conan books? The order should include both Robert E. Howard's and other authors' material.  Don't really care about comics and other non-book sources.
Is there a suggested order of reading Conan books?
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<suggested-order><conan><robert-e-howard>
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Several different authors have tried to establish a chronology, but according to  Wikipedia :   A completely consistent timeline that would accommodate every existing Conan story is impossible for several reasons. However, the stories were not published in a any particular order because Robert E. Howard meant for the reader to believe that the teller of the story, Conan, told the stories as he remembered them randomly.     There is no order in which you have to read Conan's books nor is there a definite chronological sequence. This is the case, because the books were written in a way that makes it seem like Conan is telling the stories as he remembers them.
There is no specific order in which readers should read any of Conan's books. There is no sequence to read the books in as the stories we published in a way that makes them seem as if Conan was telling the stories as he remembers them.