I forgot to mention another important class of non-archival materials that can damage the support information for mineral specimens: rubber bands, staples, paperclips and other fasteners. It is possible to get plastic and plastic-coated paperclips, and stainless steel staples are sometimes available. If you need a replacement for rubber or elasticized bands, however, your best bet is to use archival string or ribbon.
The biggest boon to collections in recent years is the availability of computer software for managing information.
It is important to back up software early and often. It is also important to have off-site backup on a regular basis, and to have a backup copy of your information in your control in case of electronic catastrophes (like the Internet becoming unavailable).
What form of back-up is appropriate? Over the years, I have stored information on paper tapes, punched cards, magnetic tape, 8-inch floppy disks, 5" floppy disks, 3.5" not-so-floppy disks, CDs of various kinds, and flash drives. Each of these media have expiration dates, due to medium degradation and/or hardware obsolescence. So as technology changes, your backup copies have to be copied or translated onto new media. This may not be a lossless process.
Similarly, the software available for documentation of your collection can change over time. These days, I keep most of my data in Excel databases; but I can remember when Microsoft Works was a better platform for graphics. In the 1970s, much scientific programming was done in Fortran, and I can remember running into problems updating a program written using unsupported features from an earlier Fortran version. Many cataloging programs today are proprietary; what happens to your catalog if the company producing your program goes out of business? Can you still get support for your software?
Finally, if you use password-protected programs to document your collection, make sure you still know the password as long as you need your backup. Heirs and executors may need your password as well.