So just how old does a coin have to be, to be classified as ancient?
The division of history into "ancient", "mediaeval" and "modern" was largely an invention of Renaissance historians. They declared themselves to be "modern" and considered everything before their time to be "mediaeval". The "ancient" age was held to have ended with the fall of the Western Roman Empire in 476 AD. It has very little practical meaning in non-European contexts, but is still often applied there by Western collectors. China, for instance, never really had a "dark age" in the same sense that Europe did.
Personally, I use the following definitions for my coin collection.
"Ancient" is anything from the invention of coinage up to 500 AD. It's a convenient break for us numismatists because in 498 AD the "Eastern Roman" emperor Anastasius I reformed the coinage, effectively beginning the "Byzantine series". Thus, everything "Roman" is ancient, everything "Byzantine" is mediaeval.
The end of the mediaeval period is somewhat arbitrarily set at 1450 AD. Some historians and collectors try to tie the beginning of the "modern" period to a specific historical event or marker, such as 1453 (the fall of Constantinople and the end of Byzantine Empire), 1492 (Columbus discovering new world), 1517 (the start of the Protestant Reformation), 1518 (introduction of the thaler coin) or 1601 (beginning of Krause catalogues).
Greetings & Salutations!
Those are good dates and historical markers too.
I think the 1400 to 1600 period is kind of a no-man's land. Some people (because of Columbus, the Reformation, etc) put that period in the modern era but on other internet lists I have seen discussions quite regularly regarding coins from that period on both ancient lists and modern world lists. Ditto for commercial websites like Vcoins.com and non-commercial ones like coinarchives.com.
A colleague of mine, Wayne Sayles has a good book out about what he calls "non-classical" ancient coins. Wayne's books are very good and avoid too much technical jargon. Wayne has been a collector/dealer for a very long time and knows his stuff. He also has a book out about Byzantine (also called Romaion) coins. They are very good introductory books on the topics.