First I need to mention that it is my impression that insurance companies will do or say anything to delay and minimize payment. Do not trust anything said to you by an agent. Anything you do not have in writing (e-mail does seem to have the power of paper today) is essentially worthless. Agents will intentionally mislead you and or make promises they have no intention of keeping. You may make decisions based on this information and find later that you made a bad choice but that it is too late to change. So get everything in writing and write down the name of every person you speak to.
Property loss compensation is subject to some very confusing rules intended to minimize payment, however (with AAA at least) the need for documentation is minimal affording an opportunity to influence the eventual payment. I was unaware of these rules and lost quite a lot of money.
The two most important considerations are "replacement cost vs. actual value" and depreciation. If you have a replacement cost policy you may be paid the cost to replace your lost property with equivalent items but you will need to replace the items within a fairly short period of time. If you can not replace an item or have no place to house it because your house is gone or uninhabitable or if you would rather have cash and not a replacement item, you should consider taking "actual value" instead.
Actual value has little to do with the actual value of an item. Actual value is based on purchase price minus depreciation. There are some exceptions for things like art and possibly some collectibles or antiques so ask your insurer in advance as to how they treat these items and be prepared for a a bunch of double talk and confusion. Get everything in writing or fight your way through your policy declarations with the help of a lawyer or two to make sense out of it.
Depreciation can be considerable. For tools (including ones that suffer no wear in time and actually increase in value) the depreciation may be 5% per year with a maximum of 80%. That wonderful Starrett tool you bought 20 years ago for $400 will be compensated at $80 even though it costs $1500 to replace today.
Now for the most helpful hints:
The insurance company is not likely to require proof of purchase price especially for an item purchased 20 years ago. They took my word on everything I claimed. I made the mistake of being honest. If you got a great deal, do not tell the insurance company, it will only reduce your payment. Present the highest reasonable purchase price for every item and set the purchase date as close to the present as is believable.
Take pictures of everything you own and keep copies where they will not be destroyed in a fire or other disaster. This may be your only proof that you actually owned the items.