Well, The Eleventh Hour is as good a place to start as any. And you've come to it at the ideal time! It's the most recently aired, first in the brand new series, doesn't spoil a thing about the previous episodes, it looks beautiful, and it's designed
specifically so that you can watch it once and join the ride without having to know a jot about what's gone on beforehand.
It's not like one of those things where you can't come in midway because there's x number of ongoing storylines - you can watch most Doctor Who episodes without worrying about continuity as it's a different story each week, but The Eleventh Hour especially is the beginning of a brand new story with no tedious strings attached - just one episode and you'll be bang up to date with the entire series. All you need to know is that it's about an alien man who travels through time and changes his face - it's funny, exciting, creepy and weird. Big ol' adventure which is entrenched in the bones of British culture. Get cracking.
If you like that, you can continue watching this series week in, week out and catch up on the rest later - or you can go back to Rose in series 1 and watch all that unfold.
...assuming you're interested in checking it out, that is. You might have just come in to tell us that you've never watched it. In which case cheers for the info.