IMSLP is the go-to online source for classical musicians. My orchestra gets scores and parts from there for almost everything we play that was composed before 1927. It would be hard to find any classical musician today who isn't familiar with it.

That said, it's sometimes worth paying for a good edition, especially for old music where the composer's manuscript is hard to read or no longer exists. The best published editions include extensive endnotes discussing the sources or why the editor made certain decisions. Oh yes, that's the other thing about classical music: most of it was written with pen and paper, which means someone has to decipher the composer's handwriting (which can be messy) and whatever shorthand the composer may have used to save the time and effort of writing out all the details. Much of it was copied by hand for the earliest performances, and only published years later. And many of the original manuscripts have been lost. So in many cases there is no definitive or "original" version, but there are multiple well-thought-out editions to choose from.

As for orchestras having libraries, the New York Philharmonic does have a digital library online for study and research purposes, containing scans of almost everything the orchestra has played in its 180-year history. It's not printable and pieces that are still under copyright are partially obscured, but it's certainly useful.

On the traditional music side, it's hard to have a definitive version of anything. What you'll find will be either basic commonly accepted versions that may still vary from place to place, or direct transcriptions of one particular performance or recording.