Start with Heir to the Empire, that is the first book in the Thrawn Trilogy. It is also the first novel ever published with Lucas' consent in the Star Wars genre. If you like it, finish the trilogy.
As others have said, there are a lot of poorly written novels in the SW EU.
IMO, anything by Timothy Zahn is worth reading:
Choices of One
The X-Wing series is excellent, but be warned there are no Jedi
The Han Solo trilogy is excellent (takes place pre-E4)
I liked the Bounty Hunter Wars trilogy (Boba Fett is the protagonist)
was an interesting read (E1 makes more sense to me after reading this)
The Lost Tribe of the Sith
is an e-book only set of short stories that I enjoyed (although the last story did drag a little). Stories 1-8 are free. The ninth and final story is only available in the compilation and that costs $6.
is a POV story. it takes place during the Jedi Academy trilogy. It is written in the first person from the perspective of Corran Horn, a former Corellian Security officer, turned Rogue Squadron pilot (X-wing series) turned Jedi trainee. If you read this you'll want to read the Jedi Academy Trilogy first.
I recommend that you stay away from the Yuzhan Vong series. Many if not most fans dislike it.
The link above goes to Wookiepedia's EU timeline.