My first lasting exposure was Voyager, while I was a kid (I was born in 1987). Our national television was buying the episodes and showing them on a TV with 1-2 years delay, I think. I watched it almost from the start, I was a kid and I absolutley loved it. I never missed an episode, and many times I wished I could be there with them on Voyager. At the beginning, I didn't even know that there are more series. I guess if I knew and I had the chance I would have watched other Star Trek series, but as it wasn't showing on tv, I had no chance to watch it then.
Then, they bought all the Star Trek series, and started showing them on TV from the beginning, from TOS, I think it was early 2000s. And I had to give it a chance because I loved Voyager, so I watched it and I liked TOS a lot too. And after that, TNG came, and that was "love on the first sight".

I absolutley loved it, even the early seasons, but especially later. It's my favorite Star Trek show now. Although I watched Voyager first, it didn't take me long to like TNG even more, I love the stories, their vision of future, philosophy, the look of Enteprise (it was a surprise for me how bright and comfortable it looked, after dark corridors of Voyager) and of course, I love the characters, and especially Data. I had a big crush on him, as seen from my avatar (and I always have a crush on him when I rewatch TNG again

).
Then came DS9, and I was really curious and looking forward to watch another, new (for me) Star Trek show - but I didn't really like the characters, I missed TNG, and DS9 characters were not likeable for me. First few seasons were bereable, but not really special or interesting. I was pretty disapointed. I also disliked the stories about faith with prophets and Kira's faith, I didn't like their politics, I wasn't interested in the Ferengi stories either, and the concept of money being reintroduced. I think until that, Star Trek for me was an utopian future, and I liked that positive vision. And when the Dominion war started, I didn't like their choices, and I started to actually hate both the show and characters. I guess after TNG philosophy and future vision, DS9 was totally different for me, and not in the spirit of Star Trek,
as I see it.
I loved seeing Voyager again later, though. And the last was Enteprise, which I found ok, but pretty bland and boring.
I voted for Voyager, which was my first Star Trek show, and helped to introduce me in sci-fi in general, and also got me to watch all the other Star Trek shows. Voyager gets it's first vote here.
