I would suggest that your familiarity with the revitalised original crew of Kirk, Spock and co. would make the 'The Original Series' novels a good starting point. Just dive in - there is a lot less continuity to worry about with TOS novels. You could do a lot worse than picking up Greg's latest 'The Weight Of Worlds'.
Thanks for the kind words. In all modesty, I do like to think that THE WEIGHT OF WORLDS would be fairly accessible to a self-described "newbie." It's a largely standalone adventure focusing on Kirk, Spock, Sulu, and Uhura.