So, Dr Who has been piquing my interest lately, but I'm not sure where to start. From what I understand, it's been going on since the sixties. That seems like a LOT of catching up to do, since I've never even seen one episode. If I do go about watching it, it's going to be a lot of work on my part (I don't have television stations). Is there a site you can watch episodes on after they air, perhaps?
Regarding "Classic Who" well, you could start at the beginning - An Unearthly Child
. But perhaps you should watch Remembrance of the Daleks
first to see what The Doctor was up to before he kidnapped Ian and Barbara. Oh, but that has Daleks in it and you won't know what they are. So perhaps watch Genesis of the Daleks
first to see how the Daleks were created and be introduced to Davros. Oh, but that has the Time Lords in it. So perhaps you should watch The War Games
first for an introduction to the Time-Lords. But that ends with a regeneration, so perhaps you should get the Lost In Time
collection of orphan episodes and watch as much of The Tenth Planet
as you can for the first regeneration...
... my point being that like any long running series or sequence of stories, the show has built up a vast mythology. But generally, the mythology isn't that important. Even in the much abused 80's knowing the series' past wasn't that important. The 20th Anniversary had a returning character, concept or creature in each of its stories, but the ratings didn't really suffer. Everything you need to know is more or less explained in the episodes.
And that's especially true in "New Who" as the revived 2005 series is known. When the Daleks are reintroduced, everything you need to know is quickly and effortlessly explained. Same with the re-introduction of Sarah Jane Smith (an old Companion) or UNIT.
And that's because the stories aren't about the past, they're still about the future. The Dalek is used to show how The Doctor could easily be as ruthless and prejudiced as his oldest, most dangerous foes. The reintroduction of Sarah Jane is really a story about Rose and her inevitable future where her relationship with The Doctor will have to end. And UNIT is used in an "invasion of Earth" type story as nothing more than colourful background concept and a quick way of getting The Doctor involved.
But that's not to say that there are some threads in the New Series that don't reward consistent viewing. Russell's five years of showrunning play up heavily the concept of the Time War and The Tenth Doctor bows out with what is clearly intended as the conclusion to that thread. Bad Wolf is used beyond just the first season's arc. Rose's dead father becomes important later. All of The Doctor's companions have their own story and character development - especially Donna, which won't be as effective or emotional if you don't follow the whole story.
So I recommend you start with the 2005 series. Enjoy the new mythology being introduced. Gasp with Rose the first time you see inside the TARDIS. Watch as The Doctor shows fear for the first time when locked in a room with a Dalek. Watch Rose go back in time and try to save her father's life and fail. See how the Doctor's influence changes a time travelling con man calling himself Captain Jack. And finally watch The Doctor twice be willing to sacrifice his life to save Rose, leading to his death and rebirth as the Tenth Doctor.
And that's just a fraction of the events in the first 13 episodes. All important moments, and all moments that will have some impact and consequence later in the revised series.
Just remember, they were still finding their feet when the new series started, and the quality is somewhat mixed. But once you get to the latter half of the season, and especially once you get to the Tenth Doctor's era you'll be watching a confident series where no concept is too big, outlandish or audacious to include. And that results in a witty, emotional and unpredictable TV programme.