You asked me:
Friend in US wants to start watching Dr Who now there is a female doctor. Which are the seminal episodes she should watch in advance? Is there one episode per season she should watch?Unless your friend is already a big fan of sf shows from the last century, she should probably start with New Who, meaning the 2005 reboot with Christopher Eccleston. One sometimes needs to be forgiving of the production values of Old Who, and it may not be right to demand that tolerance of a newbie. For what it's worth, I answered a similar question about the first eight Doctors here many years ago; and a couple of years later I polled my blog readers on their favourite stories from the first ten Doctors here (and also on their least favourite stories here). But for now, we're looking at New Who.
I think rather than one episode per season, I'd recommend that your friend try one episode per Doctor if she wants to take a quick look and see if she wants to get into the show. For the four post-2005 Doctors, I recommend the following episodes:
Ninth Doctor (Christopher Eccleston): The very first 2005 episode, Rose, is a great introduction to the concept of the show, and if you are starting anywhere it should be there.
Tenth Doctor (David Tennant): The 2007 episode Blink (which stars Carey Mulligan before she became famous) and is rated as the single best ever Doctor Who story by a lot of fans (and some days I am one of them.)
Eleventh Doctor (Matt Smith): Again, the first episode, The Eleventh Hour, is the one to watch to get a flavour of the 2010 reboot of the show with a new production team.
Twelfth Doctor (Peter Capaldi): The other three episodes that I have mentioned are all more-or-less set in comtemporary England; the 2015 episode Heaven Sent is set in the far future and features the Doctor contending against eternity on his own.
After that, I'm afraid I found it impossible to cut down to one episode per series. However I think I've selected the best from each season, and ended up recommending fewer than half of them. No doubt others will share their views below.
Ninth Doctor (Christopher Eccleston) - 2005
I think the first series of New Who is still really strong in retrospect. I have mentioned Rose already. The story Dalek brings back a key concept from Old Who (set in 2012, at a time when that felt like the far future). I also like the following episode Father's Day, which establishes some important continuity about Rose (as played by Billie Piper) for later stories.
There is then a super two-parter set during the London Blitz, The Empty Child / The Doctor Dances, which introduces the recurring character of Captain Jack Harkness.
The first series ends with another two-parter, Bad Wolf / The Parting of the Ways - the first part has not aged well, to be honest, but the climax to the season and the Ninth Doctor's farewell are essential parts of Who lore.
Tenth Doctor (David Tennant) - 2005-2010
There are three full series of Tenth Doctor stories, and a bunch of special episodes - one for each Christmas and another three which were shown in 2009. If you have to pick and choose, I would go for the following:
The second episode, Tooth and Claw, is set in Scotland, starring Pauline Collins as Queen Victoria. I'm not especially recommending it, I just wanted to make sure you didn't miss any Scottish stories. David Tennant, who plays the Tenth Doctor, is from Bathgate and sounds it in real life, but plays the Doctor in Estuary English.
School Reunion brings the new Doctor and his established companion Rose back in touch with two Old Who characters - and does it rather well, in a way which I think will pique your friend's interest in the previous history of the series. My favourite episode of the season.
It's followed by The Girl in the Fireplace, which won the Hugo award and remains very popular.
Then there are two two-parters which are both very good and vital for continuity - Rise of the Cybermen / The Age of Steel, which brings back another classic concept from Old Who, and the series climax Army of Ghosts / Doomsday, which writes Rose out in suitably spectacular fashion.
This starts with a Christmas special, The Runaway Bride, memorable for the first appearance of Catherine Tate as Donna; and then the first episode proper, Smith and Jones, brings in new regular Freema Agyeman as Martha.
Some less memorable episodes (though The Shakespeare Code is fun), including a forgettable two-parter set in New York, are followed by the excellent two-parter Human Nature / Family of Blood, set in England just before the first world war and querying the Doctor's true nature. Blink has already been mentioned.
The series ends with a three-part story, Utopia / The Sound of Drums / Last of the Time Lords. I really liked the first two episodes but felt it lost momentum at the very end.
The regular companion here is Catherine Tate, returning as Donna, and I find it really difficult to choose between the episodes. Looking back I think it is the most consistent in quality of any season in New Who. If you force me to drill down, I'll choose the opening Partners in Crime, which re-introduces Donna; the two-parter Silence in the Library / Forest of the Dead, which is particularly good and introduces the recurring character River Song; the Doctor-only tight story Midnight; and the final two-parter The Stolen Earth / Journey's End, though again I feel that the momentum was lost at the very end.
The End of Time was the two-part story that wrote out the Tenth Doctor, and wrapped up almost all of the narrative threads from the first four seasons (because the production team changed at that point).
Eleventh Doctor (Matt Smith) - 2010-2013
New Doctor and new companions Amy (Karen Gillan) and Rory (Arthur Darvill) have a really strong start with The Eleventh Hour, as mentioned above. The whole season (as was typical of the new production team's approach) is very involved, but if you are skimming probably
Same cast as previous series, but an very complex ongoing plot arc which somewhat taxed the patience of even diehard fans. The standout episode is The Doctor's Wife, by acclaimed writer Neil Gaiman, which queries one of the most fundamental concepts of the series; and another good one is The Girl Who Waited, which gives Amy's character a lot more to do.
The plot arc of the season is in the first two episodes - The Impossible Astronaut / Day of the Moon - the middle episodes - A Good Man Goes To War and Let's Kill Hitler - and the final episode - The Wedding of River Song.
Although this is probably my least favourite season of New Who, it also included two sets of very short stories which explored the time-travel elements rather nicely - the first, Space and Time, was a Comic Relief special featuring the Doctor, Amy and Rory; the second, was a series of five shorts with the collective title Night and the Doctor, of which the third and fourth, First Night / Last Night, memorably explore River Song's story further (only available on DVD as far as I know).
Amy and Rory depart halfway through the season, replaced by new companion Clara (Jenna Coleman) who also has a complex internal plot arc; somehow this worked better for me than the previous series did. There is another strong start with Asylum of the Daleks; I love the bonkers concept of Dinosaurs on a Spaceship; you and your friend will enjoy the New York angle of The Angels Take Manhattan, which writes out Amy and Rory; the Christmas special, The Snowmen is particularly memorable; Diana Rigg and her daughter Rachael Stirling are great in The Crimson Horror; and finally The Name of the Doctor very nearly manages to sort out the dangling plot lines of the series as whole.
The Day of the Doctor was the 50th anniversary special, which brought back David Tennant as the Ninth Doctor, introduced John Hurt as an unrevealed incarnation, and also brought back Billie Piper. I drove my family to Cologne to watch it in a cinema. The girls sitting beside us were talking Russian to each other. It was pretty remarkable.
(Also as part of the 50th anniversary celebrations, the original Fifth Doctor, Peter Davison, wrote a play called The Five(ish) Doctors Reboot, in which he and the other survivors of Old Who attempt to get in on the 50th anniversary celebrations. Around 8 minutes in, I am fleetingly visible in a crowd scene and immediately afterwards the camera dissolves from my son, then aged 14, to Paul McGann, the Eighth Doctor.)
Time of the Doctor writes out the Eleventh Doctor and introduces the Twelfth Doctor. Clara sticks around though.
Twelfth Doctor (Peter Capaldi) - 2014-2017
By now, basically, your friend will have either got into Doctor Who or not. If she is still jumping through the history of the show, looking for the good bits, then I think the best to watch from this series are the opener, Deep Breath; the very scary Listen, which explores the pasts of Clara and her maybe-boyfriend Danny Pink; and the rather bonkers Mummy on the Orient Express. The two-part finale, Dark Water / Death in Heaven, is also somewhat bonkers but wraps things up.
I'm afraid this series also has one of the worst ever Doctor Who stories, Kill the Moon, which I would advise even completists to consider skipping.
This series had a very different format - mostly two-part stories, of which my favourite was The Zygon Invasion / The Zygon Inversion, though the immediately preceding The Girl Who Died / The Woman Who Lived is also good. Face the Raven writes Clara out in dramatic style, and the following episode is Heaven Sent, already mentioned.
After that you'll want to see the season finale, Hell Bent, and the Christmas Special, The Husbands of River Song, for the sake of completeness.
The Christmas Special, The Return of Doctor Mysterio, is another New York story which I think will be enjoyed by people who don't take New York too seriously.
I felt that the series as a whole was Capaldi's best, introducing new regulars Bill (played by Pearl Mackie) and Nardole (Matt Lucas). The three opening episodes - The Pilot, Smile and Thin Ice are all strong, and I also particularly liked The Empress of Mars and The Eaters of Light (set in Roman-era Scotland - see, I'm still thinking of you), towards the end. The closing two-parter, World Enough and Time / The Doctor Falls, brings back an unexpected character from the Tenth Doctor's era, and sets the stage for the coming switch from Peter Capaldi to Jodie Whittaker.
Capaldi has one more episode to go, in which he will be joined by David Bradley as the First Doctor, the role originally taken by William Hartnell in 1963-1966. (Bradley also played Hartnell playing the Doctor in another 50th anniversary special, An Adventure in Space and Time, a play about how the show was originally made.)
So, Chris, that is possibly more information than your friend actually wanted. And no doubt others will chime in in comments to tell me How Wrong I Am - fifty-four years of history leave plenty of room for fannish debate. In any case, I am sure that your friend will enjoy a lot of it.