Oh, it's been a while since we got this thread... time to roll it out again.
Essentially, vess, the whole 24th century post-Nemesis continuity crosses over in the Star Trek: Destiny trilogy which takes place about a year and a half after Nemesis. That's a good place to start, if you're not prepared to totally dive into obsessive insanity.
If you are, though, let me lay out all the pre-Destiny stuff by series:
TNG - Nemesis established that Riker goes off to captain the Titan. So, this splits into two series: The Next Generation and Titan. But Nemesis also had a bunch of random character changes in it (Worf back in starfleet, Wesley at the wedding, etc), so first there's a series ("A Time To...") that explains all that. The final A Time To book also establishes some more detail about Federation politics, which is followed up on in a book called Articles Of The Federation, which is like a year in the life of the Federation's president.
Here's all of that in a vague chronology / recommended reading order:
A Time To Be Born
A Time To Die
A Time To Sow
A Time To Harvest
A Time To Love
A Time To Hate
A Time To Kill
A Time To Heal
A Time For War, A Time For Peace
(Nemesis goes here)
TNG: Death In Winter
Titan: Taking Wing
Titan: The Red King
Articles Of The Federation
Titan: Orion's Hounds
TNG: Resistance
TNG: Q & A
TNG: Before Dishonor
Titan: Sword Of Damocles
TNG: Greater Than The Sum
Then comes Destiny.
(For the record, Titan and Articles are awesome, but opinions vary about the rest. In particular, few people would recommend reading the first 6 A Time To... books; the last three are the only really important ones. And in my opinion, you can pretty much skip all of them and jump straight in to Destiny. If you only want to read the best ones, do the four Titan books, Articles of the Federation, and Greater Than The Sum, which does a great job summarizing the other not-so-hot TNG stories.)
VOY - this is much quicker. Voyager had a short-lived relaunch that took place immediately after Endgame, but the author and editor responsible both left, and it stayed in limbo until Destiny came out. So pre-Destiny, you only have four books to worry about...and quite frankly, they're all pretty skippably bad.
Homecoming
The Farther Shore
Spirit Walk: Old Wounds
Spirit Walk: Enemy Of My Enemy
DS9 - DS9 ended two years before VOY, and well before Nemesis, so it had a chance to rack up quite an impressive number of books before Destiny. Unfortunately, many are out of print, and the narrative is so serialized that you won't want to skip any. After Destiny, the DS9 timeline is jumping ahead 5 years, so picking up the new DS9 novels after Destiny might be a better bet. They are, however, uniformly outstanding, and so if you go to the trouble of finding the old ones, you'll be happy you did. Ones in parenthesis are not part of the main sequence.
(A Stitch In Time - standalone about Garak)
Avatar, Book 1
Avatar, Book 2
Section 31: Abyss
Gateways: Demons Of Air & Darkness
"Horn & Ivory" from Gateways: What Lay Beyond (the first 5 are collected in an omnibus called Twist Of Faith)
Mission: Gamma 1: Twilight
Mission: Gamma 2: This Gray Spirit (these 2 are collected in an omnibus called These Haunted Seas)
Mission: Gamma 3: Cathedral
Mission: Gamma 4: Lesser Evil
Rising Son
(The Left Hand Of Darkness, Book 1)
(The Left Hand Of Darkness, Book 2 - standalones about Martok)
Unity
Worlds of Deep Space Nine 1: Cardassia / Andor
Worlds of Deep Space Nine 2: Trill / Bajor
Worlds of Deep Space Nine 3: Ferenginar / Dominion
Warpath
Fearful Symmetry
The Soul Key
(The Never-Ending Sacrifice - more about Cardassia)
All that, chronologically, only covers a period of 1 year, so then 4 years after that Destiny happens, and the next new DS9 book in January of next year will take place an additional year later after Destiny.
ENTERPRISE - post-finale Enterprise novels are progressing nicely. There's a plot thread from them that gets picked up on in Destiny as well (this is cooler than it sounds; it's not just simple time travel), but you don't need to read these books at all in order to understand it. Read them if you liked Enterprise; if you don't, don't.
The Good That Men Do
Kobayashi Maru
Romulan War: Beneath The Raptor's Wing
(The Destiny story picks up close to the end of that last book).
DESTINY & AFTERMATH - so then Destiny happens:
Destiny 1: Gods of Night
Destiny 2: Mere Mortals
Destiny 3: Lost Souls
This follows a sister-ship of the Enterprise NX-01 starting 200 years earlier, and in the 24th century it follows the TNG and Titan crews, as well as a new ship (the Aventine) captained by Ezri Dax (which also makes more sense than you'd think it would.) And Destiny has huge, huge effects on all kinds of stories. It's also my favorite TrekLit ever, of any kind; absolutely awesome.
After Destiny, the following tales have been published (in recommended reading order):
A Singular Destiny (Federation-wide tale of political realigning)
TNG: Losing The Peace
VOY: Full Circle (starts at the end of the prior VOY books 2 years earlier, and covers that crew through the events of Destiny & beyond)
VOY: Unworthy (follows from Full Circle)
Titan: Over A Torrent Sea
Titan: Synthesis
Late this year, a 4-part miniseries will come called the Typhon Pact, exploring the political landscape after Destiny (which I don't want to spoil too much).
Typhon Pact 1: Zero Sum Game (follows the Aventine)
Typhon Pact 2: Seize The Fire (follows Titan)
Typhon Pact 3: The Rough Beasts Of Empire (follows DS9, after the 5-year time jump)
Typhon Pact 4: Paths Of Disharmony (follows TNG)
Too much information?
To summarize: The fastest, most instantly awesome choice is to just grab Destiny.
The slightly less-fast, but possibly best approach is to read the first 4 Titan novels, Articles of the Federation, and TNG: Greater Than The Sum, and then read Destiny. That gives you the most relevant background, without you having to hunt down out of print books or spend months catching up. (EDIT: Actually, Articles is out of print. Oops! Well, you can skip that one too; it's great, but if you don't like hunting for old books, it's not critical.)
The slow, but totally obsessive approach is to buy a Kindle, so you don't have to hunt out-of-print books down, and then buy and read every book I just listed. Which is what I did.
Good luck
