I really loved the Doctor Who 50th Anniversary special, which means I actually don’t have a ton to say about it. (And am thus writing this a decade after the fact in internet time.) The best recap/analysis – or at least, the one I agree 110% with – is from Tom & Lorenzo.
If you’re curious about new Who, Alan Sepinwall did a nice selection of episodes that are good to start with. (I’d swap out ‘Christmas Invasion’ for ‘The Runaway Bride’ and ‘The Girl Who Waited’ for ‘Vincent and the Doctor,’ but YMMV.) I definitely recommend skipping around and trying the different Doctors, because I’d seen several Eccleston and Tennant episodes over the years, but it took Matt Smith (and, specifically, ‘The Pandorica Opens/The Big Bang’) to hook me on the show. But the nice thing about Who is that there are plenty of points to jump on.