I highly recommend the Vanguard series of TOS stories. Incredible characterizations and plausible political conflicts overlapping the events of Kirk's original five-year mission.
I third this recommendation. The series ended with me really wanting more!! plus pocket books really made it hard to jump into the current TNG/DS9/VOY timeline because they are just sooo interconnected now with the exception of the new frontier series.
However if you want to make a start in the current timeline I would advise either Star trek Titan "Taking wing" or Star Trek "Articles of the Federation" you will be lost for some of it but memory beta is your friend there.
A must read stand alone novel is "Cast No Shadow" set after Star Trek 6
Stay away from the Star Trek Enterprise novels they could have been great but bad writing just ruined them
Anything written by Peter David
"Strangers from the sky" (darn Vulcans keep crashing on our planets before official First Contact Day)
"Flag Full of Stars"