Bank Notes in the first two thirds of the 19th century were issued by banks, trading companies and others entitled to issue bank notes. The only problem with these were if the bank went bust, your bank note was worthless. The Federal Reserve wasn't here in America yet.
"Wildcat banks" sprung up and went "bust" all too often.
Runs on banks were also a problem because people would run to the bank and have their notes redeemed for gold or silver. And the Civil War brought it's own issues into the currency market especially with the confederate banks issuing a great profusion of notes. By the end of the war these notes were nothing but wastepaper.
Gold and Silver coins seemed the wisest investment but at the end of the century, banking and how bank notes were issued began to change to our current system.
Once gold was discovered in America, a flurry of activity happened. The first gold rush was in Georgia. The first place to actually discover gold was in North Carolina, where the first mint was built that actually minted gold from America. then of course we had the Great Gold Rush out to California. In my novel "Corduroy Road to Love" being rereleased in "Blue Ridge Brides" this month, the backdrop is the North Carolina gold industry. It was a brief period in the states history but a great backdrop for a novel.
I've used money/currency in other novels for other types of twists and turns. I find it an interesting backdrop that can add a little color to our stories, as well as authenticity. Take the time to see what kind of currency was used in your novel before you include it. After all the penny might not have been invented yet.