The Animated Series - I generally consider them to be throwaway in-essential episode. Only Yesteryears approaches classic . THe one you mention The Slaver weapon is also good as well.
I just don’t feel the episodes have much tension or explore any issues to depth and hence it seems inessential compared to TOS
However saying that I do think TAS would be a good show to introduce kids to Star Trek. Remove the horror, tension, sexual innuendo and just have people peacefully resolving crisis and people from different species with different appearances working together to solve problems. I do think it works as a kid show though.
My wife loves Star Trek.
In fact normally after work, I will be “can we watch some opera”. She will be “no let watch Star Trek”
Although she does prefers TNG over TOS though and prefers the more serious tone and in her view better acting and better special effects (we alternate between TOS and TNG in our watching and we are currently towards the end of 4th season).
Although saying that she does love the odd number movies in particular Star Trek VI (her favourite) and Star Trek IV. I think with Star Trek II she wasn’t convince that Spock really was dead when that scene happened. While I was in near tears (even though I knew he didn’t die and I didn’t spoil the movie for her)
I think she enjoys the campy fun nature of TOS and finds the tropes to be entertaining
So whenever there is a red shirt landing on the planet. Make predictions whether this person will die or not and crack up laughing when they do die.
She also thinks Kirk is an overactor. She also finds some of his facial expression in his acting funny and would laugh at the expression.
SHe once asked me who you consider to be the most handsome male. I responded Kirk. Which she thinks is hilarious and she disagrees that he is handsome at all. Whenever there is a female villain and they immediately fall in love with Kirk, I will be using that as evidence that Kirk is the most handsome charming man in existence and she is using that as example of implausibility of the writing.