I'd say private ownership and trade is fundamental, inasmuch as - regardless of the society - it arises spontaneously and can only be eliminated by force, but money itself is only "fundamental" to a certain kind of society.  A society with a large population, an active economy, and easy communication over long distances could not plausibly be sustained without money... but theoretically if we were willing to go back to the bronze age, money wouldn't be necessary.