A British seed vendor pointed out that you can bake dry rice to get it even drier, and use that as a gentle dessicant.
I use silica gel, but I change it infrequently, so I hope it does not over-dry my seeds.
My seeds are in 2"x3" Ziplocs with a double-sided-printed label inside. Usually I group similar pkts together into a 3x4" or 4x5" Ziploc. Those go inside a plastic tub (2 pounds of peanuts), each tub with a theme.
For the big public stash I'm currently custodian of, there are carboard boxes or big plastic tubs for catgories like "Beans & Peas", "Other Crops", "Annual Flowers" Perennial Flowers" and "Other Categories" .
The Other Categories are things like trees, shrubs, vines, ornamental grasses, "iris & lily" and some specific things that we happen to have tons of (Hibiscus, Hollyhock).
Within the boxes, there are one-gallon Ziplock bags for alphabetical grouping or things we have tons of (e.g. Marigolds or Morning Glories).
Within the gallon bags are sometimes quart bags, always sandwich bags, to group related things. These tend to be in alphabetical order.
Within the sandwich bags are whatever people sent in, or whatever was in the stash when I took over: hand-folded paper seed pkts, commerical pkts, big or small Ziplocks or huge paper envelopes. I try to re-package any big envelope into a 2"x3" Ziplock, and preserve any information that came with it - usually just a common name.
Wher someone contributes a lot of something (saved seeds or a big commerical pkt, I split it into individual trades in 2x3" Ziplocks with as much info as I can deduce, and try to include the name of the donor and "year harvested" or "Best By" date.