A survey of the Expanded Universe really ought to start with Timothy Zahn's Thrawn Trilogy. Published in 1991 by Bantam Spectra, the first book, Heir to the Empire, ushered in the Expanded Universe proper after a long period of dormancy where the only new Star Wars material being released was for the roleplaying game by West End Games.
Zahn was an established Sci-Fi author by this point, having won a Hugo Award (back when that still meant something) and created a Space Opera series of his own with the Cobra trilogy. In the course of writing this trilogy, he worked closely with West End Games, and incorporated a lot of supplemental material into the books, establishing a cross-pollination between different products. It would take more new stories to start forming the true EU, but this was the keystone, and it was a huge success.
The setup is this: Five years after Return of the Jedi, the fledgling New Republic is struggling against a sudden surge of Imperial resistance. Said resistance comes from Grand Admiral Thrawn, an imposing blue-skinned, red-eyed near-human alien who has returned from the Unknown Regions to find the Empire in tatters and he is determined to right that ship.
Thrawn has limited resources and manpower, so he resorts to brilliant tactics and intel from a deep cover spy known only as “Delta Source” to attack against “the Rebels,” until he discovers the planet Wayland and one of the Emperor's hidden vaults guarded by a powerful, but insane cloned Jedi.
Meanwhile, Luke Skywalker has a final visit from Obi-Wan Kenobi's spirit urging him stay vigilant against the Dark Side and promises that he will find new allies. Han Solo and Princess Leia Organa Solo, now pregnant with twins, are busy flying around the galaxy doing diplomatic work when strange gray aliens repeatedly attack them, intent on capturing Leia specifically. Leia also has to deal with intrigue in the government as the stalwart Admiral Ackbar butts heads with the slippery Bothan senator, Borsk Fey'lya. Han is trying to make inroads into the smuggler scene to set up freelance supply lines that the New Republic badly needs, which leads him to smuggler baron Talon Karrde, a man who's risen to prominence in the wake of Jabba's death.
After a disastrous encounter with an Interdictor cruiser, Luke comes into an uneasy alliance with Karrde. Intelligent and urbane, Karrde's real stock in trade is information, and he knows more about Thrawn than he's willing to let the New Republic have for free. Karrde also has a mysterious lieutenant, Mara Jade, who wants nothing more in the world than to kill Luke Skywalker. Mara was the Emperor's Hand, a Force sensitive assassin and spy that answered only to Palpatine. The Emperor's death effectively destroyed her life. Naturally, she and Luke have to survive a hostile forest together.
Meanwhile, Lando Calrissian has a new business venture that is promptly raided by Thrawn, and the mole miners stolen from Lando are used in a climactic space battle where the Empire cleverly attempts to use the miners to board and capture New Republic capital ships to steal them. The New Republic repels them, but at significant cost to their own drydocked fleet.
Meanwhile, Leia and Chewie capture one of her would-be kidnappers and learn he's a Noghri, a species of lethal hunters who were sworn to serve their “savior” Darth Vader. Moreover, Khabarakh, the captured Noghri, calls Leia the Mal'ary'ush, the Lady Vader, and agrees to the dangerous prospect of negotiations with his race.
Heir to the Empire is amazing. It captures the grand space opera themes and the world-hopping pulp that the Star Wars Trilogy was built on. The pace is rocket fast and never lingers too long on mundane drudgery. The heroes are in character and growing as people. Luke is maturing as a Jedi. Leia is swamped by matters of state and imminent motherhood. Han is chafing with respectability but growing into it. Lando is up to his old entrepreneurial tricks.
The new characters are fine additions. Thrawn is the obvious standout, since he's a deliberate contrast to Vader's rage and Palpatine's gleeful tyranny. Thrawn isn't so much a “villain” as he is an antagonist. He wants order in the galaxy and sees the Rebellion (he refuses to acknowledge the New Republic by title) as rampant, violent chaos that must be quelled. His effectiveness is based on an analytical mind that would make Mycroft Holmes jealous, and he has weaponized art history as a means of studying species to find their weaknesses. Thrawn is, however, still an antagonist, and while reasonable and intelligent, he is unbending and cold with regards to his enemies. He has no interest in negotiating with the New Republic. He wants them beaten down.
The viewpoint character for Thrawn is his second-in-command, Captain Pellaeon. Pellaeon is an old veteran who served back in the late Republic and into the Empire. A competent commander, but lacking in innovation, he was the one who took command at Endor after the Emperor's death and sounded the retreat to cut the Navy's losses. Pellaeon doesn't really get what Thrawn's doing all the time, but he trusts him implicitly, and is another believer in re-establishing law and order in the galaxy.
Joruus C'Baoth, the mad Jedi clone, isn't evil in the direct sense, nor is he related to the Sith in any way. He's clearly powerful and possesses wild mood swings, but wishes to impose order as well, though with him at the top deciding what that means. He's something of a Jedi supremacist, where he sees those with the ability to use the Force as the top of the food chain. He and Thrawn butt heads frequently, but Thrawn has access to ysalmiri, little lizards that create bubbles where the Force can't work, that can keep C'Baoth in check.
Talon Karrde is something of a combination of Han and Lando. Hands-on, but with a very strong organization sense that makes his smuggler group one of the most reputable out there. He's smart and has contingency plans, and he doesn't like being caught between the Empire and the New Republic, so he tries to play off both sides. Mara too, doesn't like being caught between the two factions and simply wanted to find a peaceful place for herself when Luke Skywalker comes walking into her life and the romantic tension that follows.
The characters are great. The action sequences are good, and the grand sweeping scope is everything you could want in a Star Wars story that builds on where Return of the Jedi ended. There's a reason why people clamored for years to turn this into a sequel movie trilogy.
Its damn good, and an essential read for anyone looking at getting into the Expanded Universe.