An Unearthly Child is constructed as a very good starting point, introducing the people to The Doctor and his ways. The episode introduces us to the Cold Hill School and the junkyard in which the Doctor and Susan live. Schoolteachers Ian Chesterton and Barbara Wright are concerned about Susan Foreman, who seems to have a very alien outlook on England. She is precocious but seems to have strange gaps in her understanding of the world. They have come to her listed address to investigate. Her listed address is this junkyard, which they simply cannot grasp. Then they meet this strange gruff old man who tries to get them to leave, but instead makes it look like some kind of pedophilia or homelessness situation.
Ian and Barbara stumble into the TARDIS, have dazed and incredulous reactions. Ian is the first one to circumnavigate the TARDIS and then be astonished that the inside is bigger than the outside. Then troubles ensue and they embark on a time traveling journey.
The serial is divided into four episodes. They are entitled "An Unearthly Child", "The Cave of Skulls", "The Forest of Fear" and "The Firemaker".
The adventure they stumble into is to meet a tribe of cavemen who are looking for fire and barely understand the world. The Doctor and companions get into trouble, get out of trouble, make friends of the cavemen, teach them how to make fire, and then leave.
When Ian calls the Doctor "Doctor Foreman" in the second episode of this story, he gets the reply, "Eh, Doctor who? What's he talking about?" It was clear from this that the Doctor never gives his name and there's a question as to who the Doctor is.
The junkyard where the Doctor and Susan lived also appeared in later episodes. Attack of the Cybermen and Remembrance of the Daleks. In Attack, the TARDIS landed in the scrapyard, while in Remembrance, the Doctor followed the military detail there to deal with an unknown assailant that turned out to be a lone Dalek. In Remembrance they also visit the Cold Hill School.
In The Doctors Daughter when the Doctor enigmatically says he's had children before, was he referring to this young lady who is referred to here as his grand-daughter? The Wikipedia entry makes it clear the producers changed the character to a grand-daughter to desexualize the companionship. However it is enigmatic the statement in The Doctors Daughter.