It’s the same question you have to ask when showing the films to someone for the first time. Do you go through chronologically, starting with most people’s least favourite, or do you go in release order and skip back in time and then forward again?
With the Star Wars new Expanded Universe canon, the question you need to ask yourself is: what do I want to know more about?
If you’re interested in the time before the Empire, there’s a lot of interesting stuff in the Clone Wars TV show. You see the Jedi at their height, in great numbers fighting the good fight and coming to terms with going from Peacekeepers to Warriors. You see the toll the Clone Wars take on the Galaxy, which help explain and enrich a lot of the prequel trilogy.
If you’re interested in the rise of the Empire, the books Tarkin and A New Dawn (along with some short stories) have been put together into anthology literally called The Rise of the Empire. You also can’t go wrong with Lost Stars, a book that looks into the life of enlisted men and women, as well as the every-day lives of worlds controlled by the Empire. You get to see the Galaxy from the perspective of average people, rather than the lofty experiences of the Jedi.
If you want to know more about the big gap between Return of the Jedi and The Force Awakens, there are a whole series that come under the umbrella of ‘Journey to The Force Awakens’, including the much discussed Aftermath series that aims to show exactly what happened after the Battle of Endor.
If you’re still not sure where to start, we’d recommend the Marvel Star Wars comic series. Set after A New Hope, this series answers a lot of questions like: How did Luke continue his Jedi Training without Obi-Wan (and later, without Yoda)? How did Darth Vader find out Luke was his Son? and generally fills in a lot of gaps of what happens between films in the original trilogy. The Comic series expands beyond one story, with Darth Vader, Leia, Chewbacca and even Lando featuring in their own adventures which often overlap. The Vader Down storyline crosses over the Star Wars and Darth Vader comics. The artwork in all these series is fantastic, and really reflects the aesthetic that we all know and love from the Star Wars Universe.