I haven't watched TOS (it's not to my taste), but after watching the whole series of TNG, I liked their system of government (or least what is shown). So what exactly is their system of government, or rather, what would/should it be called?
No currency—everything is provided. Food, entertainment, shelter. No required service or job—it seemed some people didn't even have a job(didn't seem to be a need for one), but still had everything wanted provided for them. There didn't seem to be a supreme leader/figurehead either, but people who would be considered important?
To me, it seems like a utopia. It seems to me a society where everyone has access everything would be great. The goal was that once your superficial needs were met, then you could improve yourself.