With all due respect, that's not a well-directed question.
There is no single ("the") collectible coin. In addition, there are many different reasons people collect coins - some for investment, some to acquire a complete set of dates, some to assemble a set that has a theme such as flowers or buildings, and on and on.
So you have to decide why and how you're interested in coins. If you're interested in value (the most common reason), there are plenty of websites that give tons of information about values. Just a tiny selection:
www.coinfacts.com
www.coinclub.com/prices
www.coinpage.com
www.coinpeople.com
www.usmint.gov
www.numismedia.com
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.