For all but the smallest quilts, I would use UPS. They have $100 of insurance built in to the price and it is much easier to collect from UPS than from USPS if you have a problem. And their prices can be better too, at least in the lower 48. I just put in a plastic bag ad then in a box. Be sure to put the delivery address INSIDE the box as well.
I have never had one go missing. I had one delayed after I had sent it UPS 2-day, they found it and sent it out Next Day early AM delivery. It had to be there for a TV show taping.
I had another one that went COD and UPS forgot to collect the check. (I eventually got it). They did not bill me for that shipment and gave me another future shipment free.