Running stuff down off the top of my head. Some of this stuff I read quite some time ago, so I can't give more than my "ten years later" impressions...
Hand of Thrawn duology...Zahn closed the Ballantine era with these two books, tying up a lot of the unanswered questions from his trilogy. It's an easy pick up ten years or so after the Last Command, and I really like the fact that while it references EU from in the meantime, you don't need to have read any of it to get into the story. It just picks up Zahn's characters (and the OT heroes, of course) and keeps the story going. Not as good as the original, but a nice ending to the story.
X-Wing series...I'd say read 'em, there's a good long series between Stackpole's Rogue Squadron books and Allston's Wraith Squadron books. Probably the two best Star Wars authors, right up there with Zahn's early stuff. Wraith Squadron doesn't get nearly the credit it deserves, it really is a fun and engaging series. Allston is the only Star Wars author to make me laugh out loud at least once a novel.
Jedi Academy series...pass on this one. Anderson's writing is pretty much god-awful. The rebuilding of the Jedi order begins here, though, so there are some fairly "important" EU developments. I'd suggest reading "I, Jedi" instead, as it covers the same ground from an X-Wing character's first-person point of view as one of the new Jedi and actually is a lot more believable.
Courtship of Princess Leia...I found this book to be very enjoyable. Of the early EU novels, this one feels the most like a movie sequel. Opinions here vary wildly, some hate it as much as I hate the Academy books.
I'd avoid the rest of the old Ballantine stuff, it is just not neccessary and not all that much fun.
Zahn's more recent stuff...Survivor's Quest, Outbound Flight, and Alliegance were just okay. Outbound Flight is a retcon of the Outbound Flight (led by Jorus C'Baoth) into the prequel era as we now know it. It is interesting, but set in the PT era and not really fitting your requirements here. Allegiance was not what I was expecting at all, in a bad way unfortunately. It was written well, I guess, but not really the story I thought I would be getting. It's set between ANH and ESB, and it does have Luke, Han and Leia of that era, but it's not about the OT heroes.
There was also a recent novel about the building of the Death Star (called Death Star) that you can skip, unless you're a fan of those 70's disaster movies (seriously, the book is Towering Inferno in Space.) Shadows of the Empire was not a fun read, though it has aspects I found to enrich my enjoyment of the OT.
To sum up (sorry!) my suggested reading list would go like this:
--reread Zahn trilogy
--X-wing: Rogue Squadron series (Michael Stackpole)
--X:Wing: Wraith Squadron series (Aaron Allston)
--I, Jedi (Michael Stackpole)
--Hand of Thrawn duology (Timothy Zahn)
--The Courtship of Princess Leia (Dave Wolverton)