The New Orleans Mint produced United States coins from 1838-1861 and 1879-1909; however, from 1861-1865 the Confederacy owned the mint and made their own coins. They made a large amount of coins for the time but they are not easy to find now. The mint made in total 427 million coins. For comparison, the Denver mint made 4,698 million pennies in 2016.
Coins from New Orleans are stamped with a large O as shown on a half dime I own. Coins from this mint could cost anywhere from $10-$10,000 at a coin shop depending on the specific mintage and grade of the coin.
If you want to own a rare coin without spending a ton of money I would recommend getting a coin from New Orleans.
Information citation: https://en.wikipedia.org/wiki/New_Orleans_Mint