So I just found out that the classic Doctor who is streaming for free on Pluto TV. I just wanted to clarify, that in general, what I heard was that the 4-part mini serials were independent of each other. Is that correct? Like, how important is watching it in order?
"Classic Doctor Who" covers a period of 26 years, during which time the series changed radically several times.
Among other things, this means:
- Not all serials were four episodes long. The longest is Season 23, which can be considered a single 14-episode serial. At a minimum, each serial should be watched in order, as most episodes end in or pick up from cliffhangers and are not intended to be viewed alone.
- Storylines from different seasons will have very different tone, particularly between the 7 "regenerations" of The Doctor.
- Alongside each Doctor, there were different Companions, some of whom have their own character arcs.
- Across seasons, and even incarnations of the Doctor, there are recurring enemies (and sometimes friends), with plots sometimes referencing prior encounters.
In summary, it is not a series of unrelated stories like The Outer Limits or The Twilight Zone; but nor is it one long saga, like A Game of Thrones. You don't have to start at the very beginning, but will probably get most out of picking a season that sounds interesting, and watching in order from there.
In most of the history of "classic" Doctor Whoo, there was relatively little continuity between the separate serials (although not separate episodes). Individual serials ranged in length from a single episode ("Mission to the Unknown") to fourteen episodes ("The Trial of a Time Lord").* The most common number of episodes for a serial was four, and after the show's first seven seasons, four became pretty stable as the default length, although exceptions were still commonplace. Season-ending stories were often six episodes long, for example.
Within any given serial, it is definitely necessary to watch the episodes in order; within a given serial, each episode after the first begins with a brief recap of the cliffhanger from the previous episode, but that all the backstory you are likely to be given**, so unless you have seen the earlier episodes, you will probably not know what is going on.
How much continuity there was between different serials varied a great deal over the quarter-century history of the classic Who. Most of the time, you could start with a new story without knowing much of anything about what had happened in the previous one. The most obvious element of continuity that might press you to watch the stories in order is the changes to the main cast. The identities of the Doctor's companions—and the iteration of the Doctor himself—naturally evolve over time, and this makes it useful to see episodes in which new companions are introduced (or leave) in their correct broadcast orders. For instance, it might not matter a great deal what order you watch "The Robots of Death," "The Talons of Weng-Chiang," "Horror of Fang Rock," and "The Invisible Enemy" in, because they star the Doctor and Leela***. However, seeing them without watching "The Face of Evil," in which Leela was introduced, might leave you rather flummoxed by her character and appearance. To a lesser extent, it also helps to watch Leela's stories in order so that you can see her character develop. She starts as a savage tribeswoman, who believes in witchcraft and is willing to kill enemies even they might be captured or defeated nonviolently, but by the end of her tenure on the show, she is lecturing other characters about the superiority of science to superstition.
There are also certain periods within the show's history in which the makers attempted to add a greater degree of continuity from one story to the next. In the earliest days, during William Hartnell's time as the First Doctor, every episode had an individual name, and there was no way for viewers to tell whether a given story was the beginning of a new serial (except by looking for a change in the credits, to see whether there was a new writer, director, etc.). For example, the seventh and last episode of the second serial "The Daleks," ends with a cliffhanger for the third serial "The Edge of Destruction." This practice was abandoned with the later Doctors (except for a cliffhanger between the Third Doctor stories "Frontier in Space" and "Planet of the Daleks"). It therefore helps a bit to watch the First Doctor stories in order, when this is possible. Unfortunately, many of the 1960s-era stories featuring the First and Second Doctors are lost, so it is often not possible to follow the continuity from one story to the next.
Another period in which there was more inter-story continuity was season sixteen, "The Key to Time," which featured a season-long quest to recover the six pieces of the titular Key. It is probably best to watch the six stories in order, although it is only really important to see the first story, "The Ribos Operation," first (since it introduces the companion Romana and the idea of the Key) and "The Armageddon Factor" last.
During Peter Davison's tenure as the Fifth Doctor (especially his first two seasons), there was also an attempt to add more continuity to the show. Often, a few minutes at the beginning of a story's first episode would have the characters discussing what had happened in the previous serial. This is most notable in "Time-Flight," which opens with Doctor and his companions talking about the harrowing events at the end of the previous story, "Earthshock." Producer John Nathan-Turner tried to introduce more continuity during this period in other ways as well. There was a story that was a direct sequel to one from the previous season ("Snakedance" to "Kinda"), as well as a more subtle sequel story ("Planet of Fire" to "The King's Demons"). There were also scattered references to much earlier characters and serials during this period (although some of those ended up producing continuity errors, when they referred back to 1960s stories that had never been seen since their initial broadcasts and had ended up lost).
*For both of those examples it is actually arguable what the correct definition of a "serial" is, but that is a minor issue.
**In the six-episode-long "The Armageddon Factor," there is a strange recap scene in the last episode, explaining where everyone is and what they are doing, even though the characters doing the explanation could not possible know most of that information.
***If you are very observant, you might wonder why Leela's eye color changes in "The Invisible Enemy" though.