It really does feel a little rushed how she shoots off those ideas rapid-fire in the soup kitchen scene. It’s like they were trying to cram it in. I wish we could have gotten more, like a two-parter episode or something. Even so, I think they do a good job of making you feel like Kirk and Spock have been stuck there for days by the end of it.
I suppose not… but part of me still wishes they had been able to save her. Although I recognize that it wouldn’t have been as good of a story if they had.
If you find old shows charming, start with the original series and just roll with it. The original series is iconic, and it’s fun to see where it all came from.
If you want a little more substance, start with Star Trek: The Next Generation. It’s peak Trek in many ways (in terms of the whole Trek philosophy and world building).