I'd start by cataloging the whole thing, including photos. And store a copy of the catalog off-site.

Most homeowners' and renters' policies should cover the collection, though you may need to inform the insurance company if the value is above a certain level, and perhaps need to pay for a rider to cover the collection. Talk to your insurance agent. If he doesn't understand, talk to another one.

The harder question, one that I've always struggled with, is how do you value your collection?

I took it to a coin show once and asked a dealer to appraise it. He thumbed through it, not really even looking at the coins, and stopped on the last page. "What you have here is mostly what we call 'junk' coins. Except for this one. You might be able to get a few dollars for this one." He had pointed at a large asian coin.

I thought it was rather insulting... if he didn't want to appraise it for me he could have just said so.