You can create your monetary system from scratch, which has its ups and downs. Do you go the easy gold-silver-copper route, or put in the work to build something as complicated as the old British system? Go with exotic coins made of electrum or mithril?
- What does the coin represent? For a long time, the American dollar represented a certain amount of gold. In theory, you could go to the bank and get your gold whenever you wanted. Maybe a silver coin is equal to a bushel of wheat, in your fantasy kingdom. Or maybe money is a scrap of paper that's worth something because everybody believes it's worth something.
- Who claims the authority to make currency? In some times and places, it was issued by banks to represent deposited wealth - not governments. Do people melt down their jewelry to make new coins? Do they melt coins to make jewelry? Is there quality control?
- On the heels of that, do people trust the money to be worth something? This is part of why precious metals are a no-brainer for coins. They'll always be worth something, right? (or will they?)
In science fiction
Up to a point, you have the option of simply using the existing monetary system. You could use "credits" or some equally generic term. Or maybe money has gone completely electronic and it's handled by your personal AI so it's rarely mentioned.
- Are there still multiple currencies - dollars, euros, yen - or has that all been scrapped in favor of one unit?
- Did some other currency unseat the dollar and become the dominant currency?
- Does hard currency still exist? (I suspect it will last longer than expected. People like to hold things.)
Is money a headache you'd rather not worry about, in a story, or did you wrestle with some of these questions?