I have never watched 'Doctor Who.' Where should I start?

Geek admission time: I know next to nothing about Doctor Who. I've never watched an episode, and couldn't tell you anything about it except I think there's a time-traveling phone booth called a T.A.R.D.I.S. I haven't the slightest idea as to what that means.

I also know there's a long, fairly convoluted history of different permutations of Doctor Who, some of which aren't even available to watch in this modern era, somehow. That makes it hard to jump on board — it's not as easy as starting with Season 1 and going from there.

Can anyone out there be my guide to this strange world? I've heard so many good things about Doctor Who that I'd like to jump in, but I don't know how. Where should I start?