Hi Beck, this what I have done in the past. I always pack with plenty of bubble wrap and a new box. I also have the framer use a good quality plexiglass instead of glass. In fact, some of the shows I was in last year would not except glass. When going to the post office, I did not elect insurance because I was confident of my packing. I have shipped items with insurance though. It just requires you to put a dollar value on the item, and the post office will tell you what their fee is to offer the insurance. It is fairly cheap, and requires one extra little paper/sticker to fill out. A decent postal employee will show how to do it. I was never asked to verify value of what I was shipping, just how much did I want to insure it for.
One other thing I would suggest, it to ask for delivery confirmation. This is also cheap, and allows you to go online to see if your package arrived. So basically go to the post office counter, ask to ship your package first class mail, delivery confirmation, with x amount of dollars insurance. Hope this helps.