Gold and silver are actually very good materials to base a currency.
For one, they are extremely resistant to corrosion, which more utilitarian metals are susceptible to. For example, iron rusts and copper oxidize relatively quickly. Bolts of cloth rot and become moth eaten, etc. for other goods. Thus your wealth is safe from being destroyed in storage.
Secondly, they are heavy enough to pose a serious obstacle to anyone who wants to carry away an amount. If you've ever seen an ounce of gold, it is extremely small for its size.
Thirdly, it is lustrous and the human eye is naturally attracted to shiny things because they look pretty.
Fourthly, they have low enough specific heats to be cast into recognizable shapes (coins) or crafted without much knowledge of metallurgy. Aztecs weren't forging iron breastplates but they were making gold and silver jewellery.
Fifth, they are also soft enough to cleave into smaller pieces (making change in a way), which is a useful quality when you want to pay an exact sum. Pure gold is also soft enough to deform when bitten down on (terrible for your teeth), which is a rudimentary method to prove its purity and authenticity.
In the end, these are all reasons why we chose these particular metals to act as currency. However, value is subjective and the need for currency is tied with economies developing a need for a common material to "store" and exchange value, such as long distance trade and increasing production specialization within a particular locale. Otherwise, like you said, no one will want to trade shiny stones with little inherent value for a sheep that can produce meat and wool or wood that can be burned.
As far as I'm aware, it is Herodotus' history of Croesus that has the first recorded reference to gold coinage.
Now the Lydians ... were the first of men, so far as we know, who struck and used coin of gold or silver; and also they were the first retail-traders.
Herodotus Book 1: Clio [94]