I've seen the first season of The Expanse, and liked it -- but it's been my experience that the book is always better than the movie/TV series. There are a number of books in that setting; what's the recommended reading order?
The book publisher (Orbit) recommends reading them in published order.
What order should I read the series?
We recommend reading both the novels and short fiction in publication order to avoid accidentally spoiling yourself for later books.
Simply read them in publishing order.
The main novels are already in chronological order from an in-universe point of view, so if you start from Book 1 and continue trough the series, you will naturally follow the progression of the story.
Each novel don't necessarily starts immediately after the previous has ended, usually each of them is set one of two year after the previous, but this is not the strict norm. More details on this question.
Short stories and novellas are published between main novels, but they do not necessarily follow the main story chronologically, they often narrate past events and explore some characters background.
Anyway, like the publisher suggests, as reported in Valorum's answer, it is better to read them following the publishing order: these characters are first introduced in the main novels, and the short stories provide in-depth information, background characterization and world building. Reading them while already having knowledge and familiarity of the characters, the setting and the story makes them more enjoyable and understandable in-context. Also check this question.
As an example, The Butcher of Anderson Station provides background for one of the most important characters of the series, but there is little point in reading about his past until you have met him during the main novels.
So, the suggested reading order is:
- Leviathan Wakes (2011)
- The Butcher of Anderson Station (2011) [Set before Leviathan Wakes]
- Caliban's War (2012)
- Gods of Risk (2012)
- Drive (2012) [Set before Leviathan Wakes]
- Abaddon's Gate (2013)
- The Churn (2014) [Set before Leviathan Wakes]
- Cibola Burn (2014)
- Nemesis Games (2015)
- The Vital Abyss (2015) [Set between Abaddon's Gate and Cibola Burn]
- Babylon's Ashes (2016)
- Strange Dogs (2017)
- Persepolis Rising (2017)
- Tiamat's Wrath (2019)
- The Last Flight of the Cassandra (2019) [Set during Leviathan Wakes]
- Auberon (2019) [Set between Persepolis Rising and Tiamat’s Wrath]
- Unnamed final novel (Expected 2020)
- Bold marks the main novels
- Italic marks short stories and novellas
- The number between parentheses is the year of publication
- The notes inside the square brackets, if present, tells when, from an in-universe point of view, do the short stories events happen. If not present, the short story is set between the previous and the next novel.
There is also a series of "four plus one" comic books named The Expanse: Origins, published in digital edition in 2017, also written by the books' author James S.A. Corey.
They details the past and provide additional background of the four main characters that compose the Rocinante crew, plus the detective Josephus Miller.
They don't spoiler anything about the books and more or less they serve as a tie between the books and the television series (the characters are drawn based on the actors that depicts them on-screen), but they are more enjoyable IMHO if one has already some basic knowledge of the characters whose past history is here narrated. So basically, I think that one can read them anytime after having read Leviathan Wakes. See also this question.
Most of the information of this answer was taken from this series' Wikipedia page.