Here's my personal 'recommendation' list. The list comprises stories which are good while not being part of any major developments in the show's timeline. So, if someone wanted to watch Doctor Who with me, I'd pick one of these. Feel free to criticize or add to this list.
S Tier:
Inferno (3rd Doctor, 7 episodes, 1970)
City of Death (4th Doctor, 4 episodes, 1979)
Vengeance on Varos (6th Doctor, 2 episodes, 1985)
Vincent and the Doctor (11th Doctor, 1 episode, 2010)
A Tier:
The Aztecs (1st Doctor, 4 episodes, 1967)
The Enemy of the World (2nd Doctor, 6 episodes, 1967)
Here's my personal 'recommendation' list. The list comprises stories which are good while not being part of any major developments in the show's timeline. So, if someone wanted to watch Doctor Who with me, I'd pick one of these. Feel free to criticize or add to this list.
S Tier:
A Tier: