Wealth

"The currency in the World of Avatar is based on precious metals, besides from the United Republic of Nations. All nations that use currency seem to use the same metals; however, they fashion them in different shapes and sizes."

"Most nations use gold, silver, and copper pieces, with gold having the largest value, and copper the least."

Global Currencies
 'Ban' is another name for some type of Fire Nation currency; this may refer to a colloquial name used for one of the regular pieces. This terminology should be used sparingly.

Water Tribe currency can be spent in the Earth Kingdom (except Chin Village) and the Water Tribes. Conversely, Earth Kingdom currency can only be spent in the Earth Kingdom. Likewise, Fire Nation currency is only accepted in the fire nation. Merchant traders can deal in all currencies.

The Air Nomads had no formal currency that we know of; if they did have a currency, it became redundant after the genocide.

Exchange Rates
Exchange rates can be whatever the DM chooses, but should be within reason. Thinking in terms of eras should give the DM a guideline.

Before the Avatar
Presumably there was no formal currency before cities formed off of Lion Turtles, and we can assume that it took a long time after that to create a mint and unite a currency. So, the conclusion is there probably was no currency before the Avatar; goods and services were probably traded.

Second Harmonic Convergence to before the Hundred Year War
With the establishment of the four nations, governments and mints would have formed (ignoring the Air Nomads, since they had no formal currency).

The Earth Kingdom became so large and sprawling that they probably had a very active economy, due to a) the sheer land available to them, b) the large coastline and c) the natural resources available in a large area. The Earth Kingdom was united by one King to become a confederate monarchy, essentially making it one kingdom.

The Fire Nation was very rural and spiritual for a long time before becoming a unified Nation working together. During Avatar Roku's time, the Fire Nation became particularly prosperous. Their prosperity and ability to industrialise quickly came in part from their location. The volcanic islands provided an energy source for industry, as did the nature of fire.

The Water Tribes formed after merging tribes and civil unrest in the years following. They lived a sustenance lifestyle and as such didn't have a very strong economy.

The Air Nomads were nomadic for a while, but formed four isolated temples at cardinal points around the world. Due to the isolated nature of the temples, the Air Nomad economy was very small and based on sustenance.