Just pick a series and start with #1
For most TOS and TNG books, order doesn't really matter unless it's a 2 or more parter. For Voyager, DS9, New Frontier, and SCE books the order does matter, they all link back to one another. And really almost every Star Trek book published after 2000 follows someway in a series.
I've been reading Trek for a while so it's pretty easy for me to keep up with the 2 books a month they come out with. The main focus nowadays is on the TNG and DS9 novels to get a gist for the Star Trek "universe". The DS9 relaunch series is def my favorite and it starts with "A Stitch in Time" written by Andrew Robinson (the guy who played Garek). That series has to read in order or you will not know what the hell is going on. I don't really like the Voyager relaunch but it's only half a dozen books at this point so it would be easy to catch up there. For TNG, I say start with the "A Time To..." series. It's seven books that take place after insurrection and before Nemesis. The books before that don't really need to read in any order and the same goes for any TOS book except for Shatner's "Kirk Lives" series which I actually like.