Two screamingly obvious choices for me today, although I do like most of the others:
The Space Museum: I actually quite like this serial, between the early attempt at a timey-wimey plot, the active role played by the regulars (especially Vicki, who is almost gleeful at getting the opportunity to lead a revolution) and the overwhelming 60s-ness of the costumes and setting. It’s far from the best here though.
The Dominators: Again, I think this is unfairly maligned - like The Space Museum, it’s fun to watch, even if it is silly. I also think the petty workplace struggles between the two Dominators are rather wittily played, which is more than you can say for some Troughton serials.
The Three Doctors: Obvious pick 1. The first multi-Doctor story (and still the best besides The Day of the Doctor), Pertwee and Troughton are a top-notch double act, Omega is a compelling villain with very interesting lore, the UNIT family are on great form, there’s just a lovely celebratory feel to the whole thing, and it moves the show forward by restoring the Doctor’s ability to freely travel the cosmos. A classic.
The Face of Evil: Pretty good. It introduces Leela, the production is typically gorgeous for the Hinchcliffe-Holmes era, the concepts at the heart of the plot are genuinely interesting. I did find it dragged a bit in the later parts when I watched it, so it doesn’t quite do enough for a pick.
Warriors of the Deep: A mess, but one that’s not entirely unentertaining. Stuff like “Face it Tegan, he’s drowned” and the infamous scene of Ingrid Pitt going mano-a-mano (womano-a-womano?) with the Myrka is at least unintentionally funny, the updated Sea Devils and Silurians look gorgeous, and the ending is sobering. Not good, but bad in interesting ways.
Gridlock: Obvious pick 2. This is a great episode overall, but I find it almost impossible not to just leap straight to the final scene whenever I discuss it, because it’s genuinely masterful. Tennant’s best ever moment in the show by some distance, but also the most emblematic of RTD’s philosophy for it. The soap/family drama aspect is what fans usually bring up as the core innovation of RTD’s first run, but I honestly think it’s the repositioning of the Doctor as a tragic protagonist that’s had the more profound and lasting influence on the programme, looking at subsequent eras. I’ve never made the connection before now, and I don’t know if he’s ever commented on it, but you have to think there’s a link between RTD’s experiences during the AIDS epidemic and how he writes the Doctor, and this scene is the most explicit he ever gets with it. A profoundly heartbreaking moment, and one of my favourites of all time.
The Rebel Flesh/The Almost People: Not much to say here, it’s a thought-provoking concept and there’s some very creepy imagery, but not a story I’ve ever particularly thought back to or revisited.
The Girl Who Died: This is kind of like Gridlock, in the sense that the episode overall is good but the closing scenes are phenomenal. It’s not as good as Gridlock earlier on or in the closing scenes though, and it’s not breaking new ground for the show in the way The Three Doctors does.
Fugitive of the Judoon: Fun, mostly for the Jo Martin/Jodie double act, but I don’t think it’s as groundbreaking as proponents like to make out. It’s really just doing a variation of the same twist already used in The Name of the Doctor/The Day of the Doctor, and the Captain Jack plot strand is completely pointless.
The Interstellar Song Contest: Fantastic right up until the Doctor tortures the antagonist completely unchallenged and then isn’t called out for it whatsoever, which is a moment so bad it tanks the whole thing, Kerblam!-style. It’s a massive shame, because the episode up until that point is fun, witty and genuinely tense, plus it has some of the most breathtaking visuals the show has ever done.