The original series had money...IIRC, in the trouble with tribbles, the tribbles were being sold, as was the alcohol. In fact, I think there was mention made of possible profit. Also mining for money, etc.
You are right Mr.Rogers, it was vaguely mentioned. But whenever the fate of some alien was at stake, they were given transport to somewhere else without any mention of how they would support themselves or who would support them -- it was just all mysteriously "taken care of" by The Federation.
In the original 60s version, there were definitely UN implications to the Federation, but it actually played out that the Federation was more like NATO, with the Klingons being the Soviets and the Romulans being the Chinese. This simply scaled the earth to the galaxy.
Also true, Richard Kimball -- it was much like NATO. But the Federation was a unitary democratic government, and they acted as though "sovereignty" was an archaic and outdated concept that created wars.
Spock's line about "The needs of the many outweighing the needs of the few", as I said, sounds much like socialist -- and even communist-- political theory. Believe it or not, it did cross my mind at the time I heard it, but I enjoyed it for what it was -- scifi fantasy.