It would be interesting to know which series is seen most often in syndication. That would be a pretty good indicator of expected
general audiences.
The first Trek I ever watched was TOS in reruns in the mid-1980s, before TNG aired. At the time I was 12 or 13, and completely bowled over by that show. But I was an easily impressed kid, as I also thought Knight Rider was utterly awesome.
My favorites depend to some extent on which show I'm currently watching. At the moment I'm watching TNG (almost at the end of the second season), and even the first two seasons have averaged better than I remembered.
I tend to prefer long story arcs over episodic ones, and one of my favorite sci-fi shows ever is Babylon 5. So DS9 is pretty high on my list.
I also like ENT a lot, particularly seasons 3 and 4 (not counting the silly finale, whose only redeeming factor is the appearance of Riker). This has a lot to do with the fact that I like long story arcs.
TNG is very good, and definitely has the best actor of the lot cast as the captain. Even if Picard's supposed nationality is at odds with his very English demeanor and tastes (I get around this dilemma by imagining that he was sent to a British prep school at 8 and only saw his French parents rarely after that). I occasionally get irritated by the utopian nature of the Federation. Wesley's genius never bothered me either, rather the adult officers' inability to see his point until it was nearly too late.
TOS was the pioneer and started it all, but sadly its quality is probably the most uneven of the lot. For every "City on the Edge of Forever" there's a "Spock's Brain" and for every "The Menagerie there's an "And the Children shall Lead", "Turnabout Intruder" and "Space Seed"...
VOY to me is TNG lite. I'm saddened by the lost opportunities of this show, as there should IMO have been far more conflict between Starfleet and the Maquis when the latter first came aboard. Seven's story was interesting enough in the beginning, although I thought the show could easily have accommodated both Seven and Kes. To begin with, VOY was an ensemble show, much like DS9 and TNG, but in the latter seasons it centered far too much on Seven and the Doctor. And I can never forgive VOY for pulling the teeth of the most frightening enemy ever conceived in the Trek universe, or possibly in the entire sf genre.
But even an average Voyager episode is more enjoyable than most other stuff currently on TV...
When it comes to the movies, I think my tastes are unusual in that I'd far rather watch Nemesis than TWOK, even if the latter is more enjoyable without Space Seed. Khan is an arrogant bastard in both, but at least I don't have to watch a hapless female betraying her captain, her ship and everyone she served with...
First Contact is my favorite of the first ten movies. I must say I enjoyed the first NuTrek movie a lot. The second was okay. I don't hate it, but I have no real wish to see it again either, at least not yet.