I made a similar list for one of my friends who was watching all the Trek shows on Netflix, but was having trouble with getting through TOS. I'm a relatively new fan, but I've been aware of Star Trek and its characters for as long as I can remember (I'm in my 30s) and I had watched various TOS and TNG episodes on TV throughout the years. I had never sat down and watched TOS (or the movies or other shows) all the way through until around five or six years ago. I feel like I always knew I'd love it, and then of course, I did. Anyway, here's the list I made for my friend for fun, which took us about two years to get through. He had already watched through "The Return of the Archons" before he decided to not watch the whole series, so there were many in season one I would have added otherwise. My various reasons for inclusion were if an episode was: one of the best, representative of common themes, one I just really liked, good for understanding later movies/shows, outliers, well known or just infamous (whether deserved or not) ... and based on my own favorable memories of episodes, as there are some I'm still not as familiar with.
1.22 Space Seed
1.24 This Side of Paradise
1.25 The Devil in the Dark
1.28 The City on the Edge of Forever
2.1 Amok Time
2.4 Mirror, Mirror
2.6 The Doomsday Machine
2.10 Journey to Babel
2.15 The Trouble with Tribbles
2.17 A Piece of the Action (for a parallel Earth episode)
2.20 Return to Tomorrow
2.24 The Ultimate Computer
2.26 Assignment: Earth (I don't love this one, but I thought of it as an interesting outlier)
3.1 Spock's Brain
3.2 The Enterprise Incident
3.6 Spectre of the Gun (I was thinking of this as a representative "creative set budget" episode, although I think I would have chosen "The Empath" now)
3.9 The Tholian Web
3.10 Plato's Stepchildren (I actually really like this one, but I now know there are some very divided opinions on it!)
3.15 Let That Be Your Last Battlefield
3.23 All Our Yesterdays
3.24 Turnabout Intruder
and TAS's "Yesteryear"
Joe
1.22 Space Seed
1.24 This Side of Paradise
1.25 The Devil in the Dark
1.28 The City on the Edge of Forever
2.1 Amok Time
2.4 Mirror, Mirror
2.6 The Doomsday Machine
2.10 Journey to Babel
2.15 The Trouble with Tribbles
2.17 A Piece of the Action (for a parallel Earth episode)
2.20 Return to Tomorrow
2.24 The Ultimate Computer
2.26 Assignment: Earth (I don't love this one, but I thought of it as an interesting outlier)
3.1 Spock's Brain
3.2 The Enterprise Incident
3.6 Spectre of the Gun (I was thinking of this as a representative "creative set budget" episode, although I think I would have chosen "The Empath" now)
3.9 The Tholian Web
3.10 Plato's Stepchildren (I actually really like this one, but I now know there are some very divided opinions on it!)
3.15 Let That Be Your Last Battlefield
3.23 All Our Yesterdays
3.24 Turnabout Intruder
and TAS's "Yesteryear"
Joe