Per Doctor, and listing only those which are available on dvd in Region 1.
One - An Unearthly Child (*only*) - This was the original pilot. In this era, each episode had its own title, while the dvds give an overall story title. Go with only the first episode. Everything you need is there, and the following three episodes are so bad, you'll probably want to stab somebody just to relieve the pain.
The Aztecs - A solid four-parter, one of the earliest historicals.
The Rescue - Introduction of a new companion, directly after the departure of the Doctor's granddaughter Susan. It's only two episodes, and gives a decent introduction to the series for new viewers.
The Romans - Follows The Rescue immediately, and is another historical, though a comedic one.
Two (his first story is lost; the regeneration scene, about 15 seconds or so, is on the Lost in Time box set)
The Tomb of the Cybermen - Solid four-parter with Jamie and the Cybermen
The Invasion - 8-parter with the Cybermen working with shadowy folks on Earth, preparing to invade the planet. Introduces UNIT.
The War Games - epic, 10-episode story, which gives us the introduction to the Doctor's race, planet, and more. This is the final Second Doctor story with him as the current Doc.
Three
Spearhead From Space - The first story with the Third Doctor, reintroduces the concept of UNIT, intro of Liz and others. The Doctor is now confined to Earth in the 20th century, not allowed to leave the planet.
Inferno - Parallel universe versions of the main characters, not including the Doctor
The Three Doctors - Yeah, the plot itself is flimsy. It's the 10th anniversary special, and a reunion of the first three Doctors. Together, they go on a mission for the Time Lords; as a result, the current Doctor is once again free to travel time and space.
Time Warrior - Introduction of arguably the most popular companion, Sarah Jane Smith. Semi-historical, also introduction of recurring bad guys the Sontarans.
This Doc's finale is not on dvd yet.
Four
Robot - First story with this Doctor.
Pyramids of Mars - Oh just good stuff, gives us a new look on the ancient Egyptians as aliens.
The Key to Time - This is a box set, six stories, taking up the entire sixteenth season. The Doctor is given a new companion - actually, she's forced on him by the Time Lords. Her name is Romana, and she is every bit the Doctor's equal, the first woman who could stand up to him, and be right about it. Together, they are looking for the six pieces that make up the "Key to Time."
Logopolis - Fourth Doctor's finale.
Five
Castrovalva - Fifth Doctor's first story. It's *not* a good one, in my opinion.
The Arc of Infinity - semi-sequel to the Three Doctors, everyone goes to Amsterdam, and Maxil comes in to say "hi." Maxil is played by Colin Baker, who would later be the Sixth Doctor.
The Five Doctors - 20th anniversary special with the first five Doctors coming together, along with a metric buttload of companions and bad guys. No real plot, just an excuse to see everybody on screen again.
Resurrection of the Daleks - As I recall, it's the only time this Doctor met the Daleks.
Caves of Androzani - finale for this Doctor, introduction of the Sixth Doctor.
Six
His first story, The Twin Dilemma, comes out next week. It's mostly memorable because it's the first time the Doctor has tried to kill one of his companions. In his defense, she was really annoying.
Attack of the Cybermen - Cybermen plus grumpy Six, I love it.
Mark of the Rani - Introduction of the Rani. She's a Time Lady who was basically the equal and opposite of the Doctor. As brilliant as he is, but with no moral compass, she would murder everyone on a planet just because she could. And she kicked the Master's ass. Literally.
The Two Doctors - The last multi-Doctor story in the classic series. Everyone is pretty much completely out of character, but it's so much fun seeing the Second Doctor go insane.
Revelation of the Daleks - Six finally tones down his costume and works with Richard Bucket ("Keeping Up Appearances").
The last appearance of this Doctor was in the season-long Trial of a Time-Lord. The Doctor is put on trial for his life. Half the scenes are set in a courtroom, the other half are seen as memories. It does get a little tedious as the Doctor mocks the name of the man who is prosecuting him. Even the actor rolls his eyes more than once, and his commentary is hilarious as he describes just how bad the scripts were.
Seven The first story for this Doc, "Time and the Rani" is not yet available. The regeneration scene is simply painful. The actor playing Seven puts on a blond wig, there's a bit of whooshing around with camera fx, the wig comes off, and it's Seven.
Remembrance of the Daleks - Memorable mostly for tying in to the original pilot, and for the first-ever flying Dalek.
Survival - this was the finale of the classic series. Even then, it's pretty bad.
Eight - Well, there's only the tv movie. And it's only on dvd overseas, not in North America, unless you import it and have a multi-region player. Unless you're a major hardcore "must have every story available" fan, you can skip it.
(Okay,I'm not saying Who is as bad as Voyager, but you know, the campiness, the 60s, etc...)
