Since darkestboy started a thread on the last arc of Doctor Who, I'd figure this would be the proper time to kick off a thread on the first story: "An Unearthly Child."
It's a simple story: teachers Barbara and Ian are concerned about one of their students, the enigmatic Susan Foreman. How concerned? Enough to stake out a junkyard where Susan is supposed to be living. Next thing they know, they're dealing with her bizarre grandfather, brought into a police box that's actually a spaceship (called a TARDIS...Time And Relative Dimensions In Space, don't you know), and get sent into the Stone Age, where they have to deal with cavemen with British accents. All in all, not a bad way to start a legendary series.
I've gone through the four parts on the DVD from the library, as well as the pilot. Haven't hit the studio recording yet, but there's time for me. I can safely say that between the DVDs I've viewed and "The Three Doctors," the First Doctor is a little too upright for my tastes. I will say that William Hartnell does "cranky codger" quite well. In terms of canon, "bigger on the inside" is cover, as is the lack of TARDIS changing, though it isn't eloaborated beyond "huh...how come it's still a police box?" Also, there's no explanation on how the cave folk can speak English, so the whole "telepathic link" must have come later.
ETA: I have to ask...was it standard practice in 1963 for teachers to follow their students home? It just seemed a bit excessive. "Hmm...we can either crack the enigma that is Sarah Foreman, or we could go back to my place and test the springs in the bed."