Take a random original document from ancient Greece or China. Today I could presumably find its text on any number of books and websites. But how did the text exist prior to the modern day? Were most original sources copied and re-copied over the centuries? Or is it more common for scholars to have preserved the original copy?
I'm sure there's a million answers, just wondering if there's any kind of "typical" path that a document takes.
Speaking for Roman texts, they are generally re-copied X number of times. As you said, there are a million reasons why a particular text would be copied (it has a particularly unique piece of information, the author is respected, the author is a "master" of a particular language, etc.).
There are a very few original preserved texts, mainly from north Africa that were written on papyrus. Most others were copied by various scholars (pre-Christian), then Christian scholars as they become the foremost literate force in the late empire into the middle ages. For this reason, most (but not all) of the preserved material will have a certain religious value to it.