What it really comes down to what coin YOU want to collect. Any coin you find interesting is worthy of being collected. There are no hard, fast rules about which coins are collectible. Do what you want, how you want, and have fun doing it!
A coin collection is called, well, a coin collection. The hobby of collecting coins is called numismatics.
a coin collector
Coin collecting
While the president has not said much about coin collecting, he has said a lot about education and about the importance of hobbies that are educational. Both stamp collecting and coin collecting teach about geography and about important historical figures, so the chances are, he would be in favor of such hobbies.
Coin collecting
Numismatology
Lots of wear on the coin and the lowest grading possible.
RPM is a coin collecting slang for "Repunched Mintmark". It refers to when the mintmark on a coin has been struck twice, and you can see remnants of the first mintmark underneath the second mintmark.
edge of a coin with grooved lines that run around the entire perimeter of the coin
In coin collecting, it means Brilliant Uncirculated, a very nice coin, but not as good as a Proof coin.
Burton Hobson has written: 'Coin identifier' -- subject(s): Coins 'Coin collecting as a hobby' -- subject(s): Coins, Collectors and collecting, Juvenile literature, Numismatics 'Stamp collecting as a hobby' -- subject(s): Stamp collecting 'Historic gold coins of the world: from Croesus to Elizabeth II' -- subject(s): Gold coins 'Illustrated encyclopedia of world coins' -- subject(s): Coins, Dictionaries, Encyclopedias 'Picture guide to coin conditions' -- subject(s): Numismatics 'Hidden values in coins' -- subject(s): Coins 'International guide to coin collecting' -- subject(s): Coins 'Stamp Collecting for Beginners' 'Getting started in stamp collecting' -- subject(s): Stamp collecting 'Coins and coin collecting' -- subject(s): Coins 'Catalogue of Scandinavian coins' -- subject(s): Scandinavian Coins
A coin described as "Premium Quality" is an above average example.