TrekLit has one big, unified continuity that's been going for about a decade now, give or take, but don't be intimidated. This post is going to seem crazy complex, but this is literally everything you need to know.
If you want the short version: just read Star Trek: Destiny, an amazing trilogy, and the stuff that comes after it. Find it on Amazon and buy it right now. It's awesome and you'll love it, and you don't need to read anything else to enjoy it. It features four different starship crews, and a ton of other characters, and will really give you a feel for the amazing scope that the Trek novels have been going for lately.
But I always want to know everything there is to know, so if you're like me and you want the long version, well, there's a lot.
First thing: there are post-finale adventures of DS9, called the DS9 relaunch, and so far it all takes place in a 1 year period from April 2376 to early 2377. It's fantastic, but also getting a little out of print, and scheduling problems led to it losing some steam. Not a good place to start right now. If you'd like to know more, go here: http://memory-beta.wikia.com/wiki/DS9_relaunch
but skip The Left Hand Of Destiny and the comics.
Then, there's a VOY relaunch, which consisted of four pretty bad books before both author and editor moved on to other things, all taking place in early 2378. It was sort of re-relaunched, with a VASTLY better author, more recently (see below). I'd also consider those four books a bad place to start.
Everything else in the 24th century is now together chronologically following Nemesis, which takes place in 2379. This post-Nemesis ongoing continuity is totally awesome, and the high point of TrekLit in my opinion. THIS is where to start. Here's everything you'd have to read to really get all the references:
A Time To Kill
A Time To Heal
A Time For War/A Time For Peace - the last 3 books of a 9 book series setting up Nemesis; the first 6 are unimportant.
(Nemesis falls here)
TNG: Death In Winter - crew reorganization post-Nemesis
Titan: Taking Wing - first adventure of Riker's crew
Titan: The Red King
Articles Of The Federation - a year in the life of the Federation president
Titan: Orion's Hounds
TNG: Before Dishonor - these last three TNG books are unfortunately inconsistent; the only real weak point on the list
Titan: Sword Of Damocles
TNG: Greater Than The Sum
Destiny: Gods Of Night
Destiny: Mere Mortals
Destiny: Lost Souls - epic crossover trilogy about the Borg invasion, following 4 crews. AMAZING.
TNG: Losing The Peace
A Singular Destiny
VOY: Full Circle - re-relaunches VOY, starting after the Spirit Walk books and covering the next 3 years, through and past Destiny
Titan: Over A Torrent Sea
Then, coming in November, the Typhon Pact miniseries, which will also catch DS9 up to the unified 24th century timeframe.
Now, if that's too intimidating, I totally understand, and I want to make clear that you can just start with Destiny because it's TOTALLY FREAKING AWESOME all by itself. But if you're paranoid about missing references, that's the whole ongoing 24th century continuity at this point, and it's certainly easier than reading several hundred
You should also read Vanguard. It's an original series set during TOS, five books strong so far: http://memory-beta.wikia.com/wiki/Star_Trek:_Vanguard
It's like TOS re-imagined by HBO, and it's consistently jaw-droppingly awesome.