The first Doctor story that I would pick for a repeat series would be The Dalek Invasion of Earth from the second series.
The main reason for this is because it features the Daleks (and everybody loves the Daleks), but also because it features a lot of recognisable settings for people to spot (even if it set in the future) which I think is quite appealing.
It is six episodes long but, when you watch it, it really doesn’t seem like it is that long (which is something The Daleks suffer from), as it is well paced and has enough thrills and spills to keep the viewer entertained.
It is probably an episode or two too long (as was proved in the big screen version of the story which told the same story in about four episodes worth of time or so), but I think that it gets away with its six episode length with its pacing and action.
It also contains the beautiful speech which was used at the beginning of the twentieth anniversary story The Five Doctors.
I love the fact that, for me, it has the most iconic Doctor Who image. The Daleks crossing Westminster Bridge.