For a good grounding, most of these hold up relatively well in terms of story if not always production value. Stories marked with * are the bona fide classics
First Doctor: Unearthly Child, *The Daleks, The Time Meddler, Tenth Planet
Second Doctor: *Tomb of the Cybermen, Ice Warriors, *Web of Fear, The War Games
Third Doctor: *Spearhead from Space, Terror of the Autons, *The Daemons, Day of the Daleks, The Three Doctors, The Green Death, Time Warrior, Death to the Daleks, *Planet of the Spiders
Fourth Doctor: *Ark in Space, *Genesis of the Daleks, *Pyramids of Mars, *Brain of Morbius, *Seeds of Doom, *Deadly Assasin, Robots of Death, *Talons of Weng Chiang, Horror at Fang Rock, Invisible Enemy (warning, this is overly ambitious for the budget and looks terribad in places), Invasion of Time. Pirate Planet, *Stones of Blood, *City of Death, Warrior's Gate (if you want something weird), Logopolis.
Fifth Doctor: *Earthshock, Enlightenment, The Five Doctors, *Caves of Androzani
Sixth Doctor: *Vengeance on Varos, Two Doctors, *Revelation of the Daleks
Seventh Doctor: * Remembrance of the Daleks. Curse of Fenric if you need to have two McCoy stories (most are shash, or overly ambitious and have so much footage cut out that they make little sense).
Some people will say The Romans. Bless them. What a marvellous triumph of the human spirit.
There goes my Moffat-esque rise to showrunner glory.
