in terms of shows (not including the old animated one)
original or just star trek depending on if you go by dvd title
the next generation
deep space nine
enterprise but this is a prequel to original so up to you if you put this first or last
however since you've not seen much I say start with next generation however if you like a big arc the deep space nine. The reason I recommend Next Generation to start is you do not need to of seen original to enjoy it and it is in most fans eyes the best series.
hope this helps dude
Agreed about Next Gen. Although, if you know next to nothing about the Original Series, certain episodes in Next Gen won't have the same resonance with you. Like the episodes where they meet Spock, Sarek, McCoy, Scotty, etc. However, most of us probably started with Next Gen.
Maybe to get you familiar with the characters, watch the original 6 movies concurrently with Next Generation. Be warned that the The Motion Picture (Star Trek 1) is boring as hell, Star Trek 3 is mostly a plot device (Although it has good parts), and Star Trek 5 is will probably lower your IQ. 2, 4, and 6 are awesome as hell, though. Especially 2 (Wrath of KHAAAAAAAAAAAAAAAAAAAAAN!).
After that, the Original Series. It's a bit campy, but it has great character moments. Actually, you might want to wait until you can get all the Remastered Editions. You can probably watch the Next Generation movies here as well (7-10). The only really good 1 is 8 (First Contact). Generations is decent (7) and Inssurection feels like a 2 hour episode (9). 10 (Nemesis). . .not so good. I'd put it above Motion Picture and Final Frontier (5), but no higher.
After that, Deep Space Nine. Great, great show, especially if you like story arcs over the episodic format.
Then Voyager. Voyager is hit or miss. It's. . .ok, but that's it.
Finally, Enterprise. I'm going to admit that ENT is a guilty pleasure of mine, but to be honest, its more hit and miss than Voyager. Like SSJmole said, it's a prequel, but you really need to watch at least Next Gen and the Original Series to enjoy it.
After that, if you're still interested (How did you get through all of that Trek!?), the Animated Series is pretty good. It's a continuation of the Original Series and most of the actors return to do their voices. It's "technically" not canon, but Trek canon is dumb, so don't worry about it.
After that, there's numerous novels you can read, a lot of which are good. Again, technically not canon, but ignore Trek canon. You'll avoid the headaches that way.
It does, doesn't it? I hope they go with TV over Webisodes if they do it. I'm not big on Web shows, simply because I never remember to actually check to see when they're up. I like the fact that it's after the Romulan War, is AFTER Next Gen, and has an aging Enterprise with a captain that wants to restore the glory of the name 'Enterprise'. I also like that the designs are a throw back to TOS. That's an interesting concept.