Fourth
The Ghosts of Gralstead, The Foe from the Future, Luna Romana, The Justice of Jaxlar, The Trouble with Drax, The Romance of Crime, The English Way of Death, The Well-Mannered War
Fifth
Spare Parts, Rat Trap, Prisoners of Fate, The Emerald Tiger, Equilibrium, Cobwebs, Cold Fusion
Sixth
The Holy Terror, ...ish, Voyage to Venus, Year of the Pig, The Feast of Axos, The Wrong Doctors, The Marian Conspiracy
Seventh
The Harvest, Live 34, Flip-Flop, Night Thoughts, Master, The Magic Mousetrap, Colditz
Eighth
His eras are divided in four major sections (with a solo trilogy with Mary Shelley, including the amazing
The Silver Turk): Charley Pollard, Lucie Miller, Liv Chenka, and the Time War. Each are all arc based to a certain degree with some solos here and there. The truly best stories are ones that in the middle of the runs (or the climaxes).
Personally, I'd recommend starting with the Charley Pollard stories because you'll hit a bunch of great stories fairly quickly, including
Storm Warning (the first story),
The Chimes of Midnight,
Seasons of Fear, and
Embrace the Darkness, which accumulates to
Neverland and
Zagreus, which then leads to a different type of storytelling (saying more would be spoilers) and the quality drops (but still has a couple of amazing stories with
Scherzo and
A Natural History of Fear).
Lucie Miller: A bit more basic adventures but slowly build up to bigger events much further down the road which is where the run truly shines. Her first story is
Blood of the Daleks and features Hayley Atwell (where I first knew her before she became Peggy Carter).
Liv Chenka: The format changes to box sets and larger, somewhat more confining story arcs. The first one (of sixteen stories) is very hit and miss but the series gets much better after that.
Time War: I haven't gotten to them yet myself. I'm rather behind.
I don't know if that website has them, but I would also highly recommend the
Gallifrey series which features Leela, Romana (II...and I), K-9 Mark I & II, and a few other familiar faces along the very long road. I cannot recommend them enough, even if some people thought it has dipped in quality over time.