The first post-Return of the Jedi book series anyone should read is The Thrawn Trilogy: namely Heir to the Empire, Dark Force Rising, and The Last Command, all by Timothy Zahn. They are an excellent introduction to the "New Republic era" of the Star Wars Expanded Universe (EU), and notably they were the first books written in real-world time to explore this era.
But after that, what should you read?
First, be aware that the post-Return of the Jedi EU is broken up into three main eras:
- The New Republic era
- The New Jedi Order era
- The Legacy era
The New Republic era emerged organically, with many different authors writing their own individual books or trilogies. They are often unconnected to each other, failing to reference surrounding events (although care is definitely taken to maintain a consistent universe and chronology!). Partially this is because the order in which they were written in the real world does not match their in-universe order. But the New Republic era was the first EU era developed; it's where it all started. There are many great stories there, and in general they do cohere fairly well.
The New Jedi Order era and Legacy era are both coordinated efforts by LucasBooks to put together many-book timelines, with each book leading directly into the next as part of a large plot arc. So those need to be read in order. But you don't need to worry about those yet: you just read The Thrawn Trilogy, and want to learn about the rest of what happens in the New Republic era before moving on.
Here are my picks for books you'll enjoy reading after The Thrawn Trilogy. After each I will put two ratings: 1-5, my subjective liking of the book/series; and A-C, my subjective rating of how much they impact continuity (with C being greatest impact). I won't include any 1-2 books unless they have high continuity impact. I'll also include the year in "ABY," i.e. "After the Battle of Yavin."
- The Truce at Bakura (3, B) 4 ABY
- Luke Skywalker and the Shadows of Mindor (5, A), 5.5 ABY
- The Courtship of Princess Leia (3, C), 8 ABY
- I, Jedi (4, A), 11 ABY; read after X-Wing books 1-4 and The Jedi Academy Trilogy
- X-Wing (4, B), 7 ABY (mostly)
- Dark Empire graphic novels (Dark Empire, Dark Empire II, Empire's End) (3, C), 10 ABY
- Jedi Academy Trilogy (2, C), 11 ABY; read after Dark Empire, preferably
After you've had your fill of the above, here are some books I would recommend in the time period between 11 ABY and the start of the New Jedi Order (25 ABY):
- The Corellian Trilogy (4, B), 18 ABY
- The Hand of Thrawn Duology (5, C), 19 ABY
- Survivor's Quest (4, A), 23 ABY
There are a lot more books from the New Republic era that either don't have a huge timeline impact or aren't very good. You can find them on Wookieepedia. It's possible some of them are better than I remember, especially given how I read many of them in middle school or high school.
Speaking of Wookieepedia, I often find it helpful to visualize what's going on by looking up alien species there.
Anyway, after that, move on to the New Jedi Order!