I'm 28, the first Trek I saw was the Voyage Home. My Father watched TOS when he was a kid, and met Jimmy Doohan at a convention one year before I was born. After I saw Voyage Home, I got into watching TNG, then grabbed each of the TOS episodes that my Dad had collected. He didn't have all of them, there were a few that he refused to get. Eventually I went back and watched all of TOS, roughly 90% of TNG, all of DS9 and ENT, and about 85% of Voyager. To this day, I've only seen three Eps of TAS.
What drew me to Star Trek was the Space Exploration. Don't get me wrong, I like action, and I loved the Dominion War. But the exploration, in a consistent universe (or at least as consistent as it could be), was what drew me. I followed the characters, in fact I think how the characters react to the exploration is more important than the exploration itself. I am very much attached to many of the characters, even the ones I didn't like (Wesley). A TOS or TNG series set in a different race, or on a different ship wouldn't bother me much, because half of the episode for me is how the characters react to the same thing.
Personally, If I were offered a chance to colonize Mars. I wouldn't even wait for them to finish making me the offer, I'd start packing my bags and making arrangements. If Obama were to tell the world today that he was going to build a ship to explore the solar system, I'd say sign me up, I'll clean the latrines on the ship if that's what it takes to get me up there.