A lot of people don't have a good feel for what money means in the game, so here's a simple rule of thumb: One copper piece is a dollar, one silver piece is $10, and one gold piece is $100. A (2-pound) bag of 100 gold pieces, the kind of reward the party expects for their very first Level-1 mission, is the equivalent of a strap of $100 bills, i.e. $10,000. (For non-Americans, just say that a copper piece is whatever round number in your currency is close to a dollar, for example €1.)
This exchange rate is based on lifestyle costs. It is hard to compare purchasing power across very different economies, but it is easier to compare social class. The lifestyle costs and definitions on PHB pg 157-158 are the best guide to what money means in the world (I am rounding a year to 350 days to make the math easier.):
A Comfortable lifestyle is explicitly middle-class. It is about 700 gp a year. In developed countries in the modern world, roughly $70k a year is considered comfortably middle-class.
A Modest lifestyle (350 gp a year) is the equivalent of lower middle class, or working class. This is about $35k a year.
A Poor lifestyle is about 70 gp a year. $7k is well below the poverty line in developed countries, and people with that income will have lives roughly as described in the book.
Why I Base the Exchange Rate on Lifestyle Costs
First, it is easy. The book tells us how much the annual expenses are for a middle-class lifestyle, and we can map that onto the modern middle class in a way that gives us nice round numbers. 700 gold pieces is a year's salary for a middle-class person in the D&D world, so its emotional meaning will be similar to $70,000 for most of the players. Their characters should react to a treasure chest with 5,000 gold pieces the same way they would react to a briefcase with half a million dollars in cash. They are seeing absurd wealth: a thing of wild tales, epic stories, and/or sketchy characters doing questionable things.
Any approach based on historical comparisons, relative prices of items, and/or relative values of coinage would be a mistake, for several reasons.
A Very Different World
Some people instinctively approach the game like a historian. This is a mistake. You should approach it like a science fiction fan. The world is not like some time in the past, it is a wild alternate universe.
As I have said before, the game is not Medieval fantasy, and it cannot be. It is its own world. This is a world with magic and teleportation and airships and golems and spirits and other magical servants that can provide cheap manual labor. These things give civilizations that have mastered them economic and production capabilities that equal or exceed some of the things we have in modern society.
Given this, it would be silly to complain when there is some important difference between the rulebooks and the situation of some historical society, and then try to change the rules of the game to match (your perception of) history. My approach to the game is to assume that the rules as written are an accurate description of the world the characters exist in, and then try to imagine what the world would be like to produce the situation described in the rulebook, and what kind of society would emerge from those rules.
For example, consider that one of the most important facts about any civilization is the percentage of the population that is required to produce its food. Before the 1800s, over 90% of the population worked in agriculture almost everywhere in the world. With the agricultural and industrial revolutions, that number came down. In the D&D world, according to the table of occupations, 16% of the population works to provide food. In the USA, the percentage of workers in agriculture did not drop to 16% until about 1950. So on a variety of economic and social metrics, we should expect this world to be more like 1950 than pre-modern times.
For another example, the 1:10:100:1000 exchange rate of platinum, gold, silver, and copper is completely unlike anything that has ever existed on our planet. Money never works like that; as soon as anyone finds any new mine (or ancient treasure hoard) the relative prices will change. It would take a massive intervention from an extremely competent and wealthy government to fix the exchange rate in the face of those fluctuations. So I solve the problem by changing the physics of the world (copied from my Spelljammer Physics appendix, although I use this in all games):
Elemental transmutation is easy and common. One of the most basic alchemical processes is the transmutation of the specie metals (copper, silver, gold, and platinum) into an amount of a different metal with the same gp value. The 10:1 exchange ratio between adjacent metals is a basic fact of physics. For example, during a short rest, anyone with alchemist's supplies can turn 100 pounds of copper (5000 copper pieces) into 10 pounds of silver and 90 pounds of sand by passing a DC 10 check. Refining it into one pound of gold is a DC 15 check, and going straight to 0.1 pounds of platinum is a DC 20 check. Similarly, if they need 100 pounds of copper for some kind of engineering project, they can make it with 50 gold pieces and 99 pounds of sand or rocks.
Very Different Prices
The relative costs of specific items are highly variable. A lot of things that are cheap in our world are expensive or unattainable in the D&D world, and a lot of things that are cheap in the D&D world are expensive or unattainable in our world. Trying to use item costs as the basis of the exchange rate could distort things a lot, based on what was chosen.
A good handaxe costs 5 gold in the D&D world and $50 in our world. A lot of other weapons and manufactured items have similar relative costs. So using that as a basis of comparison, you would say that 1 gold is $10. With trade goods like silk and cinnamon as the basis of exchange, 1 gold is more like $5.
However, if you are in a city or town, it costs 10-50 gold for a level one or two spell (PHB 159). Cure Wounds is explicitly mentioned as a common spell that is easy to hire. So as little as 10 gold buys you the equivalent of a trip to the ER for trauma surgery. Lesser Restoration and Cure Disease are level two spells, and I would rule that they are common ones. This means for at most 50 gold, you can be cured of blindness, deafness, paralysis, poison, or any disease. If you used this as the basis of the exchange rate, and compared those prices to modern medical bills, you might conclude that one gold was the equivalent of several thousand dollars.
Given these differences, the best way to sort this out is to use the lifestyles as the base. Then think about how the characters face very different prices than we do. An axe costs the equivalent of $500: 10 times as much as it costs us. Medical care costs them a tenth as much, or even less. They pay the equivalent of a few thousand dollars for curing almost any traumatic injury, disease, or medical condition in less than a minute including the diagnosis.
Very Different Value of Specie
Many people have pointed out the value of coinage in the D&D rules is not accurate for any historical society. Gold is much cheaper in real terms (i.e. a pound of it buys much less) than in any society, past or present.
For example, in Roman times, a war horse cost an eighth of a pound of gold. In Medieval England, a knight's horse cost £5-10, and three nine-gram gold coins were worth 1£, so you would pay at most 30 gold pieces, or about half a pound of gold, for a warhorse. In the American West in the 1800s, gold cost about $19 an ounce and a good horse cost about $200, so it would take about 10 ounces (5/8ths of a pound) of gold to buy a good horse. But in the game books, it costs an entire pound of gold to buy a draft horse and 8 pounds of gold (400 gp) to buy a warhorse.
And it isn't that warhorses are unusually expensive in the rules. They have about the correct price, relative to things like armor and living expenses. It is just that a piece of gold in the game buys much less than in history. (Which means that a giant pile of dragon gold is a less absurd amount of wealth than it would be in our world.)
An interesting side note is that the earliest D&D books explained the low value of gold by saying the listed prices were the result of an inflation after the adventurers hauled a lot of loot out of a dungeon. I don't know if this was actually planned beforehand, or just a retcon in response to criticism, but it shows that people have been thinking about this for a long time.
The low value of gold lets the players find and carry around a lot of it, and it means that gold jewelry and decorations will be relatively cheap. This can be fun, but it means that gold isn't actually that useful as money, especially at higher levels. It just isn't a dense enough store of wealth. You would need to carry around hundreds of pounds of it for a serious transaction.
Suggested Worldbuilding: High Value Transactions
In my games, the standard currency for large transactions is either a 1 lb. platinum ingot or an uncommon magic item (each worth 500 gp). Either of these is called an Item, and this is the standard unit of bargaining and contracting among anyone with actual money. Beyond the lowest levels, if a government or other rich patron is paying the party to do something, they will pay in one or more Items.
In centers of civilization, stamped platinum ingots from a trusted mint are often used, but on border and frontier lands, magic items are the norm. Unlike metal ingots, they cannot be shaved or counterfeited or debased. Unlike gems, they have a single known value, with no difficulty in appraisal. They are a known indivisible quantity, and anyone can verify that they are pure and functional.
In other words, uncommon magic items are actually money: They are a unit of account, a store of value, and a medium of exchange. They fill these roles much better than any other kind of specie or trade good. They fact that you can wear them and they do useful things is a bonus.
Most governments have a formula for one or more uncommon magic items that can be produced using materials they have access to, and a set of staff and workshops devoted to producing these items. These items are often a primary source of government revenue, power, and influence. If the party takes a quest from a government, or from someone in its capitol city (the one with the magic item mint), they are probably going to get paid in the item it produces. Sometimes the item will be desirable, and sometimes not (The king thanks you profusely and gives you a padded adamantium briefcase with ten Eversmoking Bottles.), but either way it should lead to a fun story.
The reward item will almost always be known to the party before taking the quest. Roll on Table F (DMG pg 146), but replace anything that weighs more than a couple pounds or has a class requirement with a d20+80 roll on Table B (rerolling consumables or armor). When doing worldbuilding, it might be useful to roll ahead of time for what item or items the various governments mint, and think about how that would affect their societies.
The further away you get from the mints, the more varied the mixture of items will be. Roll separately for each item, using the heuristic above.
When doing this, the party will reliably end up with a lot of uncommon items, many of them useful. In order to maintain balance, hand out fewer treasure hoards. My games usually revolve around patrons hiring the party for specific jobs, rather than delving through dungeons for loot, so finding big lootable piles of treasure is quite rare, rather than something that happens several times a level.