I'm only now starting to get into Star Trek (and it's various spin offs). My mom is a fan of the original with Capt James T. Kirk and my dad is a TNG/Picard guy. I haven't seen enough of all of it yet to declare a favorite. Let's just hope it all stays available on Netflix some I can get all caught up without having to buy the multitude of seasons and series.
Sites like this really come in handy.
Star Trek Minutiae.com - the Starfleet Academy stuff is pretty cool, because it breaks down those hard to understand astrophysics
And these are just awesome for the pretty ship pics.
Starfleet Ships 1
Starfleet Ships 2