Great question, and a very hard one to answer! There's a degree of controversy between various fields on the origin of money, and even regarding what "money" actually is. So uh, I'm going to just answer your side question instead, which is much simpler!

The earliest coins - set weights of precious metal stamped and standardized by a central authority - are Lydian stater starting around 600 BCE. It might way out of date, but I enjoyed this article on dating the earliest coins and I haven't seen anything recent that contradicts it.

Note that precious metals with standardized weight had been in use as currency for perhaps two millennia before coinage: the Lydian innovation was in stamping each unit of metal with some official seal. The Mesopotamian shekel, for instance, was a measure of weight, equal to a certain amount of silver (or barley, or any convertible good) which might be found in the form of a spiral coil or bar. By utilizing a standardized metric of value across many types of exchanges of various goods, the economic administration of the temples and palaces could be conducted with orderly and taxable regularity. Coinage was a further refinement in the substitution of convenient metals for standard units of worth, in that it provided a guarantee that the metal was actually what it appeared to be, and not just a cleverly silver-coated lump of rock. Actually, the composition of Lydian coinage may have been another mark of assurance alongside the ruler's impression. They used a unique blend of silver and gold called electrum, which has a distinctive coloration. I once heard a claim that natural Anatolian electrum has a much higher percentage of gold than the Lydian stater, which suggests another function of official coinage: controlling your economy via the manipulation of value and metallic purity.