THIS SOUNDS LIKE THE BEST EPISODE. And that kind of sucks about the BBC not letting them put in that subplot, but I can't say I'm surprised, seeing as it took the British government until, like, 2009 to issue a formal apology for what happened to the real Turing. :/

Definitely watch the very first installment of An Unearthly Child, though you can skip the other three if you want.
You can just watch part of the serial? Is the plot not very important?

Also, Martha is in fact the best. :D *high five*
*returns high five* :D