I think you'd do well to contact a professional archivist for their advice. You're talking about preserving these works "forever". The current formats used - digital files, printed hard copy on cheaply made paper imaged with printer toner are likely the poorest ways to keep materials. Forget the digital files for the long haul - good hard copy is where it's at, as I see it.

A well known university should employ the person(s) you need to talk to.

Finale 25 can open older Finale files. Plugins and fonts may no longer be compatible. You have all sorts of options from there. Otherwise, you should engage the services of an expert who knows how to do this.

As to long term archival, good luck with that. No one has come up with a proven, perpetual archival process for digital media that can be guaranteed. 

Thank you for your helpful suggestions.  I have now downloaded Finale 25 and can read some of the Finale files, which is great!

However, for the older files which were on an old mac called "Power Mac G4" I am getting this error message:

"You can't open the application "Finale 3.2.1 Power Mac" because the Classic environment is no longer supported."

I do still have the Power Mac G4 at present. https://en.wikipedia.org/wiki/Power_Mac_G4 

Any advice would be much appreciated.

Make sure that .mus is attached to the file name.  It will not open in OS X otherwise.

Open the file from within 25.

it is probable that, once opened, much of it will be blank. Finale has changed default fonts over the years. Change the fonts to Maestro.

I still keep a G4 for legacy files that need to be converted. They're handy to have around. To do so, you should convert it to a dual-boot system with OS 9 on one partition or drive and OS 10.4.11 on the other. Not all G4s handle Leopard very well and some can't run it at all.

If you can't get Finale 3 files to open after following my earlier suggestion, try this:

You will find much "abandonware" at Macintosh Garden. I saw Finale 2000 there which should run in OS 9 and open Finale 3 files. Make certain that any files you save in 2000 have .mus appended and that the font is Petrucci.

http://macintoshgarden.org/

The LibreOffice Project is a freeware consortium. LibreOffice is touted as an alternative to Microsoft Office but I don't use it for that. It is pretty cool for those of us with legacy files, however. It will open AppleWorks except for the graphics module, MacWrite, Word 5.1 (best version ever) and many other types of files (not ClarisDraw, unfortunately, but that will open on your G4 in OS 9).

https://www.libreoffice.org/

If that still doesn't do it, feel free to contact me directly through the Finale Forum.

http://www.finaleforum.com/viewforum.php?f=5