Lemurette - Star Trek on TV was a huge phenomenon that lost popularity over its last decade, but there is still a hard core of fans supporting the novels. Since the TV shows were cancelled the novels have got rather more engrossing as the authors can take the show in new directions and effect real change.
And we have some VERY good authors. Two of them have already responded to you.
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'.
You've got a lot of pleasure to look forward to with the later shows too - The Next Generation is fantastic, Deep Space 9 is my personal choice, Voyager although not my favourite show has some superb recent novels by Kirsten Beyer, and Christopher (see above) is about to present us with his hugely anticipated relaunch of the prequel series Enterprise - Rise of the Federation.
Feel free to ask questions - most of us fans are pretty friendly, and how often do you get to converse with the authors you are reading ? That's a bit special !