14. Ghost Light 26.5-26.7
I choose Ghost Light primarily because it typifies that relationship between the Doctor and Ace. It illuminates his efforts to help her grow, and their mutual frustration in the inevitable difficulties that result. It is perhaps the most mentally taxing Classic Who serial, and among the most relationship focused. We can see a new level of personal understanding in this story, which Classic Who by and large avoided. It was exceedingly rare up until now for a companion's struggles take centre stage. Just like in the efforts of modern Doctors to deal with the domestic, we see the Doctor struggling to understand how traumatic it is for Ace to face her fears in this familiar but now alien filled landscape. I think this disconnect is one of those important elements of the Doctor's characterisation. It is not quirkiness that makes him truly alien but his insensitivities. I think it is important to note that like just in Modern Who examples, his hearts are still in the right place. He is wanting to make Ace the best person she can be. I imagine disagreement already, but I would say it is one of the strongest Classic Who examples of the Doctor trying to be "the man who makes people better" to quote the Master.
13. Rose 1.1 
This story is noteworthy mainly for being an introduction to Russell T. Davies brand of Doctor Who. It brings the audience into his values for the programme. Doctor Who to Mr. Davies is about real people with real human lives who happen to fall into an alien experience. It is the first step toward a version of Doctor Who that explores that the people Doctor takes with him have not only jobs but families, and lovers, people who matter, lives of their own before he and his TARDIS intrude. The story is framed to give us companion Rose Tyler's perspective on events as they unfold, thus providing a new kind of entry point. The narrative is built so a first time viewer of needs no foreknowledge of Doctor Who and will be no more in the proverbial dark than the characters are, a statement that is true of many Classic Who stories, but far fewer Modern Who ones. Other important bits include the Doctor's unique and quotable response to Rose asking who he is, thereby setting us up for a bunch of slow reveals about what it is like to be inside the mind of a Time Lord, as well as a string of hints regarding the Last Great Time War.