There's also the original show, which ran from 1963-1989, and the TV movie from 1996. They're all in the same continuity, although given it's a long running series there are of course some 'canon hiccups (As with Star Trek).
The classic series though is very low-budget, so be prepared for that, there's a lot of cheesy effects, sets etc. and the writing is not quite as complex as new Who (with some exceptions). The 60s (which is in black and white) started the series, with William Hartnell and Patrick Troughton but unfortunately a lot of that era is missing

although the show from the seventies on is intact (although some of the Pertwee era suffers from color loss). The Seventies for many is often considered the golden age of Doctor Who, with two popular Doctors (Jon Pertwee and especially Tom Baker) in the whole decade. Despite some production updates, the show struggled in the 80s, and was cancelled in 1989 with Sylvestor McCoy in the lead. The original show is also in a different, 'serial' format, with multi-part stories, usually in length from four to six episodes (Each about 20-30 minutes each), with about five stories per season.
The 1996 TV movie featured Paul Mcgann as the Doctor (With McCoy returning to regenerate), but didn't launch a new series. Finally the series was brought back in 2005 with Eccleston (Although the fate of the Mcgann incarnation wouldn't be revealed until 2013's short "Night of the Doctor").
Doctor Who has also had spinoffs. The first, K-9 and Company, only lasted one episode in the 80s and featured popular companions Sarah Jane Smith and the robot dog K-9. More sucessful was "Torchwood", which also focused on former companion Captain Jack (John Barrowman) and a team of alien investigators. The show ran for four seasons. There was also Sarah Jane Adventures, which also featured Sarah Jane, which ran for five seasons until the unfortunate passing of the lead actress, Elisabeth Sladen.
Doctor Who's also got of course, a lot of novels and also a long-running audio drama series in which a lot of the previous Doctors and companions participate.