What is the best way to store this equipment? Is there a storage system that works well for photographic equipment?

The best method for long term storage of photographic equipment is to place it in a temperature stable, low dust, low humidity environment with plenty of fresh air circulation. Lenses even benefit from occasional exposure to UV light through the optical path to discourage the growth of fungus on the lenses' elements.

No case provides those last two requirements, so any solution that involves enclosed cases is not an ideal one. If enclosed cases are used for other considerations then some form of desiccant should be used to absorb the moisture that was in the air at the time the case was closed.

Most large rental houses store their lenses unboxed on open shelving in a room with the same type of temperature/humidity/dust control that one typically sees at a data center where server racks are located. If one doesn't have the capability for such exotic environmental control, then a storage cabinet is usually the best solution. Again, the use of desiccants or other humidity control measures should be used (unless one is located in a very arid climate) and the cabinets should remain closed when there is the possibility of a lot of dust in the air (such as when one sweeps the floor or vacuums the carpets).

That said, is there an argument for having a storage method for home (e.g. large metal cabinet) and a separate one for travel (e.g. large camera backpack)

Yes, please see above.