This is one programme I will always watch (the one exception) because I've been a fan since I was 8. Just to point out, there are far more than 174 episodes if you take into account the original series that ran from 1963 - 1989. I started watching in the early 1980s, with Peter Davison (the Fifth Doctor) but my favourite was Tom Baker (the Fourth Doctor), whose stories were sometimes repeated, or else I saw them on video.
The original series is made on a shoestring with some embarrassingly bad visual effects, but the characters are great and the plots and ideas are often brilliant and groundbreaking (and much copied).
Still, for a newbie, I recommend starting with the 2005 series, with the episode Rose, and moving forward from there. It's pretty damned brilliant for several series. However, the episodes over the last four years have been a lot more hit and miss though, I have to say.
More on Doctor Who here, if you want a thorough introduction from yours truly (link bombs away). :)