Regarding "canon", I think what you're really concerned about is "continuity", you want the books to matter, and the vast majority of novels published since 2001 have been in one large continuity. There are occasional gaffes, much like the TV shows, but the novels do all hang together, refer to each other, and explore consequences of each other's storylines.
It's an amazing universe, more unified than the TV shows could ever have been, and (for my money) often grander in ambition and more successful in execution. In particular Star Trek: Vanguard, set on a space station during TOS, and Star Trek: Destiny, a recent (2008) crossover trilogy that finally has the Borg invade en masse.
The flowchart that ryan linked you to is also in my signature; another boarder, 8of5, and I put a lot of work into it, but it shouldn't intimidate you. Almost anywhere on that entire flowchart is a good place to jump in, and then explore earlier works or later works following arrows in either direction.
Aside from Vanguard or Destiny, a couple common starting points are at the beginning of the DS9 relaunch (which is fabulous and a great interconnected storyline) or, if you're less interested in reading so many different novels, the "A Time To..." series provides a jumping on point to the more interconnected post-Nemesis continuity. Most people recommend skipping the first 6, though, as they're fairly unimportant and not really up to par. Starting with A Time To Kill is where I'd recommend jumping into the post-Nemesis storyline.
One thing the flowchart doesn't have is recommendations for quality, but almost everything on there is up to the standards of the TV show or higher, in my opinion. The first 4 Voyager relaunch novels are generally agreed to be weaker, I mentioned that the first 6 A Time To... novels aren't up to the same high stakes as the later 3 and everything that flows from there, and the Stargazer series is fairly shallow. New Frontier, over on the right, is an idiosyncratic take on Trek that reads a bit more like a comic book, with ridiculous occurrences and over-the-top characters, and isn't for everyone (though I loved it). Everything else on there has my recommendation. Just pick what interests you and dig in.
And keep posting questions. A lot of the authors will post here and the community in general is really helpful!