Deep Space Nine has a lot of internet backers. Boogie likes it a lot I seem to remember from back in the gaf days. I think it starts off shitty also but everybody says it get better and stronger as it goes on.
I skimmed this thread earlier, and was going to leave it alone, but since I got a shout-out, I guess I should give my spiel.

Short version: Yes, DS9 rocks.

But I also loved TNG.
Long version: I'm a very strange Trek fan. As a young kid, I was 8 or 9, and my dad rented STIV: The Voyage Home. Then I watched Wrath of Khan, and then I got into TNG.
So I am (was) an uber Trek nerd who never really watched the Original Series. To this day, I've probably only watched 7 or 8 full episodes of TOS. Of course, being the nerd that I am (owning the Star Trek Encyclopedia and Episode Guide) I have read everything about every TOS episode anyway.
But yeah, I grew up originally on TNG and the original movies. I think TNG was lightning in a bottle, in so far as it was
perfect sci-fi for someone to be exposed to in their formative years. Without a doubt, I owe my "geekdom" to TNG more than any other work of fiction. Does that mean it would stand up in quality in 2012 to someone who's just getting into Star Trek? I'm not sure. But it's still worth a recommendation.
As for the original series movies, they're all worth watching. 1, 2, 4, and 6 on their own merits, 3 just because it bridges 2 and 4, and five, because, well, as benji said:
Next came DS9. And yeah, as Stoney suggested, I think it kicks ass. Some of the best character work in 90s television. Sisko is a badass. Garak remains one of the best characters in sci-fi. (seriously, in the Pale Moonlight is a classic for these two). It stole the best from B5 when it comes to arc'd storytelling.
Voyager. Voyager was near-complete shit. I watched it straight through season 4, and then more or less dropped it. And for context, up to this point, I watched Trek religiously. EVERY episode of TNG, DS9, and Voyager. But sometime after season 4, I came to realize.....this show wasn't really any good. It was a chore to watch. Voyager does have some good episodes. Maybe a dozen or so. But apart from that.....Voyager is what started to end my love affair with Trek.
Enterprise. I watched about a season and a bit of Enterprise before I realized that it was even worse than Voyager. Then I watched a few episodes in season 4 because everyone was saying the show had turned around under Manny Cotto, and they were sort of right. But other than that, the show was completely worthless. For Groo to say he "loved" the series is totally incomprehensible to me, and I can only assume it is nearly the only Trek that he has watched, and that all of the Trek that came before should blow his mind compared to Enterprise.