Where to start?

Star Trek: The Original Series {TOS} - Ran for three seasons, 1967-1969. Its a fourty four old sci-fi show, so don't expect Avatar-esque like effects :P The episodes are mostly, if not all, unconnected to each other & there's some pretty good vintage sci-fi viewing in there. It has been recently enough remastered on Blue Ray, & the effects have been replaced with CG ones if thats your posion.

Star Trek TOS-era Movies: Six movies, picking up after the tv show ended. 2,3 & 4 form a loose arc & should be watched in order. 2 & 6 are by far the best.

Star Trek: The Next Generation {TNG} - Set about 70 years after the events of the final TOS era movie, TNG is a new ship & a new crew. It ran for seven seasons, & again, the majority of the entire series is episodic & there's no big story arcs. TNG's first & second season havn't aged all too well {they are 26 years old!} but after that the show hits its stride & really raised the bar for Star Trek. Very highly rated show, again though, you have to stick with it through its shaky roots.

Star Trek: Deep Space Nine {DS9} - Ran concurrently with TNG from season 6 onwards. Its set in the same time-frame as TNG & focuses on another entirely new crew. This time however, its set on a fixed location, a space station that doesn't travel around...adventure, comes to it! The station is beside a stable wormhole, that leads to the other side of the galaxy, & that allows further development. Like TNG, its beginnings are weak up until about season 3 {though season 2 had some fantastic eps}. but it seriously hits a stride from then on. Its the first Trek to introduce a very long story arc, in the form of a war which runs until the very end of the show. Its absolutely brilliantly brilliant stuff, & prob my personal favourite. Its a darker, gloomier setting & explores everything from Religion to War.

Star Trek: Voyager {VOY} - This ran concurrently with DS9 from about season 5/6 onwards. Its about a ship named Voyager, that is thrown from one side of the Galaxy to the other...& its entire seven seasons is one long story arc about their journey home. Again its an all new crew on an all new ship. Its set in the same time frame as TNG & DS9, but there's very little crossover given how far away the ship gets stranded. I've done a recent enough rewatch of this, & like the previous two...its starts terrible but does improve. I enjoyed it a lot by the time I'd finished, & feel it got a worse reputation that it deserved. Its worth watching, but TNG & DS9 are largely superior.

Star Trek TNG-era Movies:

Star Trek: Generations - This was the first of the TNG era movies, it aired after TNG had finished on tv.
Star Trek: First Contact - This came next, was a far better effort.
Star Trek: Insurrection - Third outing for the TNG crew on the big screen. Not as good as First Contact.
Star Trek: Nemesis - The final TNG movie. None of these movies, perhaps except First Contact, require you to actually know anything about Trek. Though its prob best you avoid these until your more familiar with it.

Star Trek: Enterprise {ENT} - This is a prequel show, that was chronologically the most recent one, but is set about a hundred years before TOS. Its about the very beginnings of Trek, how it all got started etc. Obviously a new crew & ship...though this only got four seasons. It gets a lot of flak from fans, but its actually a great show & by the time it was hitting the fourth season, it was well up there with TNG imo.

Star Trek: XI - This is a reboot of Star Trek & a JJ Abrams film. Its set in the TOS era, featuring the TOS crew {obviously different actors} but is set in an alternate timeline to the already established Star Trek. This allows it to do whatever it wants as its separate from everything else that came before it. There's a sequel to this film coming out in Summer, Star Trek Into Darkness.