I just thought I might broaden the thread a bit too. I'm curious and have been thinking about changing things up as well (buying more, outgrowing my current setup).
So, I guess it comes down to what you are trying to protect them from? Theft, Fire, Flood, Moisture, etc.
Some may consider "safe storage" to mean protecting them from falling into the wrong hands (kids at home, neighbors, break-in, etc.).
If that's the case, maybe starting with a home security system with a zone dedicated to the firearms cabinet (that kills 2 birds; theft and access). Then considering additions like
A secured closet might work from some people but not all. Then you can get into locks, supports, backup access, etc.
Trigger locks and cabled to something structural might be the answer (similar to how a gun store locks up at night).
Additionally, ammo may be locked and stored separately (so kids can't load guns or play with ammo).
Other folks may be more concerned with the environmental, depending on your climate. So storing them:
Not in a location such as a basement that might take on water.
Desiccant packs or rods.
De-humidifier
Still others may look to protect from fire (which seems that you might be leaning towards). Again - just trying to add to the larger discussion. I might pick up a tip or two.