I would suggest that the attempt to pigeonhole Biblical Christianity into a political or economic system invented by the "pagan" world could sufficiently describe the acts of the Holy Spirit in the Book of Acts.
Having said that, you left out communism- "a system in which goods are owned in common and are available to all as needed." (Merriam Webster). That would seem closer to the situation presented in the Bible. The problem with any and all of these worldly systems is who or what is regulating the system.
(As an aside, you also forgot the Mosaic Law's economic system.)
Now, the government in Acts is upon Jesus' shoulders and was regulated by the Holy Spirit. That is to say the "government" was not of human origin and therefore was free of corruption. The two who tried to corrupt it dropped dead.
You see, the "big three" of capitalism, socialism, and communism are really Economic Systems. Mankind's political systems have many weak spots, giving opportune ways to manipulate them all, because Mankind obviously has an incessant lust for power, prestige, and wealth.
Intellectually, it is futile- if not foolish- to compare or to attempt to reconcile God's way with those of fallen Mankind.