I've listed most of the post OT books in order, and starred the "important" ones. More stars is more important, in my opinion. This is excluding X-Wing books, which I think can be read on their own. Books marked with # are ones that I haven't read but I've always heard sucked.
1. *The Truce at Bakura
2. *The Courtship of Princess Leia
3. **The Thrawn Trilogy
4. **The Jedi Academy Trilogy
5. *I, Jedi
6. #Children of the Jedi
7. #Darksaber
8. #Planet of Twilight
9. #The Crystal Star
10. The Black Fleet Crisis Trilogy
11. #The New Rebellion
12. The Corellian Trilogy
13. *The Hand of Thrawn Duology
14. **The New Jedi Order series
15. The Dark Nest Trilogy
16. Legacy of the Force series
I also didn't include the Junior Jedi Knights and Young Jedi Knights series which take place before NJO, but they're young adult books at best, and aren't that important, nor that good. I'd just read the Wookieepedia entries on them.
I've also not read the Black Fleet Crisis or Corellian trilogies, so I don't know much about them. However they don't seem to be mentioned much in NJO, so you could probably skip them if you want to dig into NJO that much sooner. A lot of people don't like NJO because of its premise, but I think they're very well written, regardless.
I haven't finished NJO yet so I don't know about the latter two. Legacy of the Force isn't even fully written yet.
Bassoon, n. A brazen instrument into which a fool blows out his brains.