Let's talk about the materials that surround your minerals. These include: boxes, labels, packing material, repair materials, and documentation. All of these could decay over time, possibly damaging the specimens themselves, or losing their accompanying information.
Newspaper is a common wrapping material, used to protect specimens while collecting in the field, and while transporting from mineral shows to your home. It's tempting, in the field, just to write the collection details -- where, and what date -- on the paper itself. The problem with this non-archival material is that it decomposes over time; paper made from wood pulp turns brown in sunlight and gives off acidic fumes. Eventually, the paper flakes into small particles. Some newspapers also have ink that can rub off on specimens, discoloring them. And the acid from the paper can react with some minerals.
Other materials used to wrap specimens in the field include butcher's paper (or shipping paper, toilet paper, paper towels, tissue paper...), dry-cleaning bags, canvas bags (used by many field geologists), beer flats, and film canisters. Almost all inexpensive paper is pulp paper, and will break down forming acid over time.
Cardboard boxes are frequently used to store individual specimens; beer flats for transport are also cardboard. In my experience, cardboard is more durable than paper with regard to exposure to sunlight and heat, but it is not a permanent material, and is again wood-pulp based. Archival cardboard boxes are available. Sometimes plastic trays are used, but not all plastics are archival, so check the material before you decide to use it.
Fragile specimens are sometimes kept in boxes padded with cotton or polyester fibers. Cotton is not archival and subject to insect damage, and any fibrous material can get caught up in specimens with points or cavities. An least one museum of my acquaintance pads specimen boxes with an archival closed-cell foam material such as "Volara."
Many collectors use wood cabinets. Some woods, like oak, give off fumes over time, so are not archival for containers. (The British Museum used to recommend mahogany.) Also, some finishes give off volatiles.
What about labels? The paper may be pulp-based, so non-archival; the ink may be unstable to sunlight, and fade away; the label may have been previously torn and repaired with cellophane tape. Cellophane becomes yellow and stiff and loses its stickiness over time. (Other tape kinds can be even worse, like old duct tape, which leaves gooey residues.) Some collectors save old labels in mylar or other archival envelopes, because they are valuable to the provenance of the specimen, no matter what they are made of. But for your new labels, try to use archival materials.
Older specimens sometimes were repaired with non-archival glues, or coated with yellowing shellacs. Modern epoxies and UV-setting resins may be more permanent. Another repair technique is to use an adhesive that is easily soluble in something the specimen is not (e.g., casein glues for non-water-soluble specimens), so that the repair is not permanent and can be redone if there is a later need to do so.
Finally, on the subject of preservation of documentation, we need to discuss computer files. This will be a separate blog entry.