It wasn't arbitrary.
It was driven through the market by their properties.
They're both elemental, so they're utterly divisible and still combinable, with no change in those properties.
They have high unit value and sufficient rarity to serve as a medium of exchange even in high value economies.
You want to carry $3000 worth of pig iron in your pocket, or across a border?
Governments (princes) got into the game because they realized they could 'clip' the coins, and thereby profit running the mints and using the law (taxes) to force the use and collection of their money. But they started with putting their imprint on the coins of the type already arrived at by the market (gold and silver, depending on scale of transaction).
They always do insofar as no one has been in a Beyond Thunderdome scenario, where tomorrow is going to be essentially worse than yesterday, because nothing is being produced anymore, just everything cannabilized.