Hi Dudley
What you choose to store your material in will depend on what you need - is it likely that you're going to need a water and fire resistant safe? Do you get bushfires in your area, or torrential rain/cyclones?
I would recommend against the use of a fire resistant safe. I have seen the aftermath of bushfires here in Canberra and can attest to the fact that these safes act like ovens when faced with very hot fires that last longer than about 30 minutes (the safes are only rated as 'reistant' for a short period of time). At several workshops run by the conservators in Canberra after the fires, quite a few people came in with carbonised blocks of photos and documents that had been in these safes. The flames hadn't got to them, but they were as good as burnt to cinders.
I can recommend a layered approach to packaging. This means that each document will be in its own archival quality folder or wallet, and photos in pockets in an album or similar...then store these inside either an archival board box, or a large plastic storage tub (you can buy these at supermarkets etc.) They will be quite safe, and if stored up off the floor on a shelf in a cupboard in an area of the house that has a stable environment, there should be no incursion from damp or water, or insects for that matter.
Archival board boxes are not water proof, but in the event of a water disaster, the boxes actually soak up quite a lot of water before the items inside start getting damp. The layered-packaging approach means that even if water starts to seep in, there's another layer of protection for the documents before they start being affected directly.
If you live in an area with extremes of temperature and/or humidity, there may be other concerns to take into account, so I would recommend talking to the conservators at your local/state library, archives or museum for advice.
Please remember to scan or photograph all your treasures and keep digital copies of them yourself, and give another copy to someone else in the family. Then if something terrible (heaven forbid) should happen at your house, at least there will be copies preserved for the future.
I hope this helps.
Cheers
Prue