Several caveats; Don’t clean the coins, Keep them together in some boxes and handle them with white gloves or a sweat sock to keep finger oils off the coins. Take pictures of them to send to a remote appraiser and to establish that you had them (proof of ownership). If you are going to keep them, organize them into coin flips and tubes, and make notations on the contents, condition, and dates. Consider getting a safe, to keep them together and secure. (coins can weigh a lot, too – keep that in mind).
Selling to a reputable dealer, collector, (or pawn shop) is the fasted route to liquidating your collection for cash. Keep in mind that these buyers are looking for values below market, to reduce their risk and make a profit on the eventual sale; you may be offered between 10 and 70% of the retail value of your coins.
If you have the time and ambition, you can use the internet for valuing your coins, and sell them on your own. Craigslist, EBay, and some of the popular coin sites (forums and for sale sections) are your best options.
US coins are backed by the might and presence of the US government. The US Mint produces all the coins and distributes them through regulated channels, and at high security.
In the UK, according to the Royal Mint: ”
The cost of producing United Kingdom coins varies according to the specification of each denomination. The value of metal in each coin accounts for a large part of the total cost, but it is also necessary to take into consideration the broader costs of the manufacturing process. These vary according to the complexity of the coin. The Royal Mint does not reveal exactly how much it costs to make specific coins as such information could be used to its competitors’ advantage.”
While there is speculation that mints worldwide have similar issues to the US, I will focus on US coins. It is generally acknowledged that the mint spends more on manufacturing pennies and nickels than than they are worth.
The coins (and notes) are minted to be as unique and resistant to copying as possible. As such, many of our minted coins are made of valuable metals vs. cheap alloys. sometimes these metals exceed the value of the coins. Even “cheap” metals, like zinc (used as a filler to reduce the copper content in a penny) have increased in cost over time.
Production is in the US, by Federal employees, paid on government pay grade. Private companies and other governments may be able to produce cheaper coins, but these are not backed fully by the US Government…
You can use a coating for your hands, like Pro-Tek Invisible Glove Lotion.
Edited from my Quora answer, June 28, 2017