The 3 claims were not baseball card related but limited edition art prints shipped in tubes. Each claim was in the $200-300 range, and was paid within a week by the USPS.
I ship probably 100-150 such items each year, and of the 3 claims I filed, two were for damage, and one was for a lost package. I shipped them all via PayPal click-n-ship, so the records were already online. Just had to go to the form here:
http://www.usps.com/insuranceclaims/domestic.htm and completed the necessary information.
All I had to do was describe what was in the package. For the lost package, no photos were necessary. They never asked for further proof beyond the info I provided. For the two that were damaged, I provided a single photo for each showing the damage.
For value, there's a site a lot like VCP for art. I just pulled the 6-mo average price off that site and used it for replacement value.