To be honest, I always wanted to get into Star Trek, but I never could. I watched several of the movies, but they didn't manage to hook me up.
Just like with SW people need to base their opinions on their own viewing, for Trek I would do as the others suggest and start with TNG. Afterwards, you can decide if you want to go back and watch TOS. Honestly, if you don't mind 60's camp I'd start with the The Original Series and then move on to TNG. Then you move on to Deep Space Nine, arguably the best Trek series, but again it's debatable. Voyager comes next and is honestly one of the worst Trek shows but there are still a few good episodes here and there. And, finally there is Enterprise the lowest of the low and the one that comes first chronology. But, if you're committed then you can watch it too it's not complete horse shit but it is is seriously bad.
Now, as for the movies it's a mixed bag and everyone has their own opinion. For me, I think all of the TNG movies are utter and complete crap that try and make the series into action schlock. But, there are plenty of great TOS movies. I'll rank them as follows, again this is my OWN opinion:
-Star Trek: The Motion Picture (#2); A lot of people told me this movie was boring crap going in but when Mr. Plinkett did a review of the 09' ST movie he said it was one of his favorites so I decided to check it out. As it turned out he was right it's great IMO. Yes, its slow and "boring" but if you like TOS TV show then you should like the movie which is basically just a high budget extended episode of the TV show.
-Star Trek II: The Wrath of Khan (#1); My favorite and most Trek fans would agree. What's funny is that I liked you originally sorta watched it one day without any knowledge of the TV show and thought it was crap, badly acted and cheesy hilarious. Yet, after I watched the TV series and came back I cried at the end. It is an amazing movie but you have to have a connection to the characters to care or understand them.
-Star Trek III: The Search for Spock (#6); It's an alright movie don't have much more to say.
-Star Trek IV: The Voyage Home (#5): A great movie with a really fun plot, it shows that ST isn't just about space battles and what not. But, is about a solid story and fun characters.
-Star Trek V: The Final Frontier (somewhere near the bottom); Directed by William Shater, Starring William Shatner and pretty much crap.
-Star Trek VI: The Undiscovered Country (#4); Another one of my favorite and the last of TOS movies. It really takes the original crew and gives us one last great mission with them.
(NOTE: After this comes the TNG movies I wont rank them because I think they are all crap)
-Star Trek 2009 (#3); My third favorite Trek film and the least Trekky of them all. JJ Abrams takes Star Trek to the big screen once more and basically turns ST into Star Wars. And yet, it's a great fun ride. It's mindless, senseless fun with a great set of characters. The fact that die hard fans can't accept this change for the big screen is the only problem.
-Star Trek: Into Darkness (shit); Not even worthy of a rank really, all that fun adventure stuff and generally decent plot that JJ managed in the first movie is lost here. Instead, we get a plot that seeks to rip off the best ST movie while also being boring and nonsensical. All the lens flare and big action can't save the stupidity that is this movie.