I always use UPS - they have tracking every step of the way if you are nervous like me. And built in insurance, and I find their rates cheaper. But like someone said, DON'T go to a UPS store - go right to the depot.

Be sure to put a second address label INSIDE the box, maybe in the bag with the quilt, in case something happens to the box.

i've been shipping quilts through our postal system for almost 10 years now- i guess i've been lucky- i've never had one damaged-missing or even late-
i always send them priority mail- with insurance and delivery confirmation.
my only question about using the vacuum bags is...can you actually fold the bag then to get into a box? my vacuum bags are stiff--stiff after i remove the air.
i use a kitchen plastic bag- make sure you put an index card inside the package with to and return addresses on it= a phone # wouldn't hurt either
it has been the most cost effecient way to go- i did try a couple other carriers (because of customer requests) they were alot more expensive- and we were not all that happy with them- so now i stick to the post office-