[Spoilers ahead, obviously.]
I was asked recently how somebody familiar with 21st century Doctor Who might best approach the 20th century back catalogue. A comprehensive answer to this is more a book than a blog post.
The short answer is: not chronologically. The 1960s black and white stories were produced on a treadmill of forty-odd episodes a year, and while there are some magnificent gems to be found there, even the hardiest binge-viewer of pre-Star-Wars sci-fi will find themselves losing the will to live at times. And there are large stretches during the colour years that varied between uninspired to awful. But that answer still leaves one with no clear direction.
When I was about to hit my teens with a dull thud, the Australian Broadcasting Commission (as it was then known) ran repeats of Doctor Who every weeknight at 6:30pm, just before the 7pm news. But there seemed no rhyme or reason to their selection, beyond not showing black and white episodes. (Here in the 1970s, we're modern, and we have a whole range of colours at our disposal like brown, and orange, and some other shades of brown. You should have seen the period-appropriate decor in my house!)
In the 80s, perhaps belatedly realising the extent of the fan base, the ABC ran every complete story available, which at the time still ill-served the 60s. The BBC had, in a canny anticipation of the Thatcher years, rationalised their use of video tape and storage space by junking those episodes not deemed significant. I'm not unsympathetic, because for my own part these repeats were taxing my ability to shoplift blank VHS cassettes at the required rate. Which led me to make some difficult decisions about which stories were worth keeping for posterity.
So, informed by the fact that my own fandom was initially acquired through an arbitrarily incomplete, post-60s selection of stories, and later by having to decide whether a given story is something I'll want to rewatch endlessly, I think the best introduction is to use the sequential runs of stories I suggest below as a way to get a broad sweep of the program before filling in the blanks. Or else you can pick any one of these as a landing point, and proceed as you wish.
Series 7 + Terror of the Autons
We have a fresh start with a new Doctor in Jon Pertwee, new production team, and a less taxing schedule of 26-ish episodes per year, which would remain more-or-less standard until the mid-80s. Also, in 425-line black and white, a few upturned plant pots, some boxes and loo rolls will pass as an alien city, but this wouldn't cut it in colour. So the decision was made for the Doctor to be stuck on Earth, and for the tone of the show to reflect an audience that had started as young children becoming young adults.
The first story of series 8 (I will not succumb to the revisionism of calling each series a "season"! A ghastly Americanism!) marked a return visit of the Autons from the previous year, the first appearance of the Master as a recurring foil for the Doctor, and the introduction of new companion Jo Grant.
There was also a step back from the grittiness of the previous year, and an increasing cosiness to the Doctor/Jo/Brigadier/UNIT setup that wasn't entirely a bad thing, but it did get a bit baggy after a few years, and needed a refresh.
The Green Death + Series 11
The refresh arguably started in the final story of series 10, which threw labour disputes, environmentalism, alternative lifestyles, and artificial intelligence into a big, eerily prescient melting pot. Oh, and it's the one with the giant maggots.
Also it's the last story for Jo, who has blossomed into a mature, but still accident-prone, independent woman, and discovered she doesn't need the Doctor any more. Well yes, technically she's married off to a young man because Katy Manning was leaving the show, but it's done in a way that suggests she's chosen to move on to new horizons, and the Doctor's stiff-upper-lip but very apparent sense of loss is quite tear-jerking.
The next series kicks off with the introduction of Sarah Jane Smith, and the iconic diamond logo and time tunnel opening credit sequence. There's an unprecedented thematic unity to this series which carries on from the Green Death, about the consequences of exercising power from a position of ignorance, which is a bitter pill the Doctor ultimately has to swallow. Also. poor old Captain Mike Yates finally gets a character arc after several years of no discernable character with which to arc. There's so much power and subtlety to this series that you almost forget the rubber dinosaurs and Pertwee's silly "Whomobile". (Seriously; it was his. He had it built at his own expense.)
Series 12 + Terror of the Zygons
Tom Baker was without question the perfect actor for the part, and he defines the role to this day. Also, the Doctor, Sarah, and Harry Sullivan are the best Tardis team. They get put through the wringer in this series, in a way that is revealing of character and makes you love them.
You don't even notice that only two of the five stories in this series are actually good; the characters and the actors who play them are so beguiling. Mind you, those two stories have been sometimes equalled, but never bettered. They are spectacular, and tell you everything you need to know about Doctor Who.
The first story of the next series is the third in this run of classics.
Again, it's nothing special in the plot department, but in terms of setting, design, casting, direction, it was spectacular.
Tom's first three-and a bit years were glorious. After the departure of his first producer and script editor, and the apparent recognition that both of these jobs were a poisoned chalice that led only to burn-out, if not nervous breakdown, things went off the rails. Also this was the late 70s and inflation meant that an adequate (if not handsome) budget at the start of the year, split equally between six stories, meant a shoestring budget by the end of the year for the last one or two.
City of Death + Series 18 + Castrovalva
Compounding this was the fact that Tom was becoming more proprietorial about the show (i.e. impossible to work with), and the appointment of Douglas Adams as script editor for series 17. On the face of it, this sounds like a winning combination, and it was — but mainly for the one story I include here as unrepresentative. The City of Death was put out under a pseudonym, but mostly written by Adams. It's silly, and a blatant send-up of the show, but unlike other stories of the period, it works beautifully.
The appointment of a new producer and script editor for series 18 was a breath of fresh air. There was no way that a mostly studio-bound, shot on 625-line tape production could match Star Wars, but there seemed to be a determination to play a different game just as well. The was only one dud story in the series, and even that had Judge Bullingham from Rumpole deliver a hearty kick to K9, so it wasn't entirely without merit.
Like Pertwee's last, this series has (along with a new title sequence) a thematic unity that became increasingly dark and funereal after Tom tendered his resignation and, much to his surprise, had it accepted. The fact that his enviably libertine lifestyle was taking its toll, and had visibly aged him compared to just a year ago, only added to the sense that this Doctor's time was up.
This series is often criticised for being dull and humourless. Those criticisms are wrong. The dialogue is every bit as witty as anything that had come before and, given strong material, Tom is working with it rather than against it, and we get a swansong for the powerful, passionate Doctor of his first few years. Maybe much older, tired, and aware that his time has come, but fighting till the end, and it's beautiful.
I include Peter Davison's first story here, because it concludes a trilogy that reintroduces the Master after a long absence. Also because I really believe that Peter's performance here in another debut that's light on story but full of character (if with some clunky supporting performances) is just as remarkable as Tom's. Peter is the first actor to play the part having grown up as a fan (to be followed by Tennant and Capaldi), and it shows.
People can be quite dismissive of Peter's Doctor because he's not a character actor like Hartnell or Troughton, or a comic actor like Pertwee, or a force of nature like Tom. I think he's brilliant in Doctor Who and a load of other roles, but in Who he was not well served by an increasingly directionless production team after the script editor on Tom's last series left. So what with Peter's short stay with the show, there isn't a solid year of stories to recommend.
The Turlough Trilogy + Peter's Last Stand
The series 20 run from Mawdryn Undead, to Terminus, to Enlightenment is another neat trilogy. It's a character redemption arc for new companion Turlough who (spoiler alert) isn't entirely trustworthy. We get the Brigadier back for a new decade, lose Nyssa who's been with us since series 18, and also have the magnificent Lynda Baron as a thigh-slapping, heartily laughing, buccaneering space pirate. (The latter of whom will have you questioning your sexual orientation if it isn't already oriented toward thigh-slapping, heartily laughing space pirates.)
Davison's last three stories in series 21 are a character redemption arc for the Doctor. Tegan, who has been with the Doctor since Tom's last story, concludes that travelling in the Tardis is not good for one's mental health, leading to some soul-searching for the Doctor. Then we have Turlough leave to deal with some unfinished family business, and we take on new companion Peri, and another final battle with the Master (as far as we know…).
And then we have Peter go out sacrificing himself for his new friend in a story by someone who'd written for the series from the 1960s through the seventies and masterminded Tom's glory years.
Sorry Colin
By all accounts, Colin Baker is the loveliest person you are ever likely to meet. I've seen interviews with him, and can confirm that he appears utterly delightful.
None of that carried through to his performance as the Doctor. A few of his stories were quite clever, but he was given bad direction on how he should play the part, the idea being that he he should contrast likeable Davison by being as unlikeable as possible, and he certainly fulfilled that brief. Nobody competent had been in control of the show since Tom's last series, and the show had been running on luck, inertia, and Peter's personal charm and ability to elevate patchy material.
There is no Colin Baker story that is a good entry point for a new viewer. Even dedicated fans should put on protective clothing before going there. Take that as a dare if you wish. Hell, start with Timelash if you think you're hard enough.
Remembrance of the Daleks + Series 26
Which makes it all the more remarkable that the series recovered. A new script editor was appointed simultaneously with a new Doctor, Sylvester McCoy. His pitch for creative control of the program was a desire to bring down the Thatcher government. Which wasn't necessarily the most relevant attribute in a nominally lightweight creative endeavour, but given the government at the time was determined to kill public broadcasting, turnabout is fair play.
The BBC had already decided to kill the show. In 1970 the move from 40+ episodes a year to around 26 was on the insistence of the production team to allow more time to produce a better quality program. The switch to 14 episodes a year in the late 80s was imposed on the production team by a corporation eager to help the public forget the show and not miss it when it was gone.
But Doctor Who would not lie down and die. After a wobbly but promising first year for McCoy, it hit the ground running, opening his second series with a story that hit all the Doctor Who tropes, and moved the Dalek/Nazi analogy uncomfortably close to home, with the Daleks using a bunch of gullible Mosleyite fascists as their bridgehead to 1960s Earth.
Did I say the best Tardis team was the Doctor, Harry, and Sarah? I was wrong. It's the Doctor and Ace.
Series 26, McCoy's third, and the last, is the most sophisticated the show has ever been. Nothing in the 21st century can touch it. It's about growing up, trauma, sexuality, trust, eugenics, and explosions. It's also got the Brigadier, the Master, homicidal furries, and Nicholas Bloody Parsons!
Series 26 is 14 marvellous episodes of Doctor Who distilled. It's arguably the model for all 21st century Doctor Who. That show should have gone on to greater heights, but by 1989 the Thatcherism that the program had been satirising for the past few years meant that the only remaining in-house BBC productions were news, sport, and Doctor Who. And the decision was made to keep news and sport.