1. Scheduling: A scientist friend once told me to expect everything to take three times as long as you expect. The need to move a collection is often due to outside forces: a reorganized academic department, a new home, etc. One very common reason is the sale or donation of the collection; work with the former owner (or estate) to make sure you have the time you need. If you are shipping specimens from one place to another, make sure there is an appropriate place for the containers at the receiving end.
2. Help, and the lack thereof: A quote often seen in fiction goes, "Friends will help you move; good friends will help you move bodies." You are likelier to need help packing than transporting. Such help should be experienced with minerals (or else you should keep the delicate specimens away from most assistants), enthusiastic, and above all trustworthy. They should be able to follow your orders rather than deciding to improve those orders without telling you. You may need friends or volunteers to help if you have a tight schedule; on a very tight schedule you may have to rely on paid professional movers.
3. Packing: Two considerations are the distance the collection must travel and the elapsed time that it will stay packed. When I moved about 80 boxes of specimens from Massachusetts to California in the 1980s, I shipped some through the mail in cardboard boxes, some in wooden crates (and cardboard boxes) that went in a moving van, and one flat of delicate this-end-up mineral specimens stayed in our car as we drove across the country. I packed individual specimens with their labels in paper (especially toilet paper), plastic dry-cleaning bags, and sometimes cotton box liners; better materials are probably available now. Field collected specimens were often wrapped in newsprint. The collection stayed in their boxes for about a year before unpacking.
4. The dropsies: The rule of thumb I heard years ago about packing boxes was that you should plan for the contents of your package to survive a fall from a six-foot height onto concrete. If you have visited a post office at Christmas-time, imagine those other boxes being dropped onto yours. A specimen unable to survive such treatment should be shipped another way. There are stick-on detectors that measure the amount of force that your package has been subjected to.
A famous mesolite specimen of my acquaintance was supposedly shipped from India while sewn into a wooden box and packed in soap flakes; it had its own first-class airline seat. Which brings us to...
5. Transportation: How will your collection move? Is your carrier secure against theft and damage? Is your collection safe at the temperatures (and possibly pressures) it is likely to be exposed to? Will it be detoured or derailed by hurricanes, snowstorms, or floods? You may wish to divide the collection into separate units to be transported in different ways.
6. The destination: Is the destination ready to receive your collection? Sometimes this is not possible, as when an old museum is renovated. In that case, where will the collection be stored until its destination is ready? What are its conditions like, in terms of environmental control and security?
How will your collection be delivered? Is access adequate? Is there a risk of items disappearing from the loading dock, or of dropsies as boxes are carried upstairs?
7. Unpacking: should be done with at least as much care as packing. Have a plan and a place set aside for dealing with broken specimens. Listen for crunching sounds and feel for unexpected softness as you unpack.