If you’re going to watch the original run, be prepared to be patient and endure a bit of padding in even the best stories. A combination of low budgets, cramped studios, generally slower pacing in pre-MTV era series, and the serialized format (necessitating that stories get dragged out sometimes an episode or two longer than the story requires) all together can sometimes cause modern day viewers to grow impatient. My advice - watch all the stories as episodic installments, one episode a day, rather than in the “movie format” versions how they were shown in the mid-80s.
William Hartnell - Part One of An Unearthly Child is a great introduction to the series, but the rest of that serial is forgettable. The Daleks, of course, but IMO the Dalek Invasion of Earth was the best early Dalek story. tThe Aztecs was a terrific historical story, and the Time Meddler showcases a villain who was a pre-cursor to the Master.
Patrick Troughton - Unfortunately, scant complete serials survive. But the Mind Robber was a particularly imaginative story, and the Krotons was decent. The War Games has it’s moments (especially the final episodes showing the first TV series appearance of the Time Lords as a race.)
Jon Pertwee - the Silurians, Inferno, the Daemons, the Sea Devils, the Three Doctors, Frontier In Space and the Time Warrior
Tom Baker - The Ark In Space, Genesis of the Daleks, Terror of the Zygons (if you can forgive the infamously bad Loch Ness Monster), the Seeds of Doom, the Deadly Assassin, the Talons of Weng Chiang, the Sun Makers, the Pirate Planet, Warrior’s Gate, the Keeper of Traken and Logopolis.
Peter Davison - Castrovalva, Kinda, Earthshock, Mawdryn’s Undead and the Caves of Androzani.
Colin Baker - Vengeance on Varos - That’s all. (And that’s being generous.)
Sylvester McCoy - Didn’t see much of his run, but I’ve heard that Ghost Light was supposedly pretty good.
Quite honestly, I’m surprised that “City of Death” is such a fan favorite. I never considered it to be too memorable - save for the Paris location shots and a guest appearance by John Cleese (rather than the story itself.)
What to skip, the worst serials of each Doctor era: the Keys of Marinus, the Dominators, the Time Monster, the Invasion of Time, Time Flight, Twin Dilemma (and everything else during the sixth Doctor’s time except “Varos”), and Dragonfire. Also, don’t bother with the 90s era Fox TV movie - a complete mess from start to finish (too bad though, since Paul McGann shows he could have made a terrific Doctor given good or even halfway decent material to work with.)