We have a safe deposit box for things like passports, SSN cards, and the like. I would have kept the fireproof lockbox - we leave the key in ours. That way if someone breaks in, they'll see that there's nothing of value to them, and leave the box behind because it's too bulky to take. I keep sentimental things in there, and things like credit cards that can be easily cancelled when stolen.
For paper filing, I use a system called "Freedom Filer." It's pricey at $45, but for me, it was a good investment. It is color coded to tell you what to shred after a year (CC bills, utility statements, etc), what to shred after a new copy comes in (insurance policies, health policies, etc), and what is permanent (medical records, school records). It takes the guesswork out of what to keep. 95% of the paper we keep will never be referenced ever again.