Too young to like TOS IMHO. special effects are old and dated as is the acting/music/directing styles.
A classic is a classic is a classic.
"Dated"?
Everything is "dated" that isn't contemporary, if one judges solely by that.
I would argue that Leonard Nimoy's character of Spock isn't dated, and, had the franchise the guts to go with the unnamed female First Officer portrayed in The Cage, (played by Majel Barrett), that, along with Lt Uhuru (possibly the first black woman ever depicted as a commissioned officer on a TV show), along with the conflicted character of Spock, would have made it even more timeless.
Some of the stories are excellent; some, good, while some, inevitably, have dated poorly.
However, I will argue that "Enterprise" (which I thought underwhelming in the extreme) will age a lot less well, CGI, notwithstanding, than does (or did) ToS.
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That's exactly my concern, and I don't want to put them off.
@Scepticalscribe Is Mirror Mirror the one with the alternate universe and bad Kirk and Spock, etc?
Is it just that it was a great episode (which I think I recall it was), or is there more to it that's needed?
Also which one was City on the Edge of Forever?
The Cage, I think I recall. It sets up the first Enterprise captain as Pike. Not sure how much that matters?
Mirror, Mirror was the alternative universe (Spock with a goatee, but still with integrity and a moral compass in an alternative universe, though he would have argued he was governed by logic, not ethics); City on the Edge of Forever was brilliant - an alternative history story that won awards (the same award that The Inner Light won for STNG years later).
Do you worry that they (your children) are too old or too young?
A good story is a good story, and doesn't need CGI or special effects to be told. It will hold its audience anyway.
My quarrel with most of the movies is that they fail to tell a story, and, instead get lost in spending their budget on blasted and bloated special effects and CGI, - instead of telling a story and making the CGI secondary to that - which, frankly, makes them instantly forgettable.