USPS is the cheapest, with the least damage. UPS and FEDEX next. UPS stores will not ship guns. USPS and FEDEX will. When you insure a package it requires a signature to receive, they will ask extra for adult signatures. Delivery in the AM is extra, most stores aren't open till 10 /11.
You can ship guns through these carriers by law. Handguns can only be shipped for repairs. I use FEDEX alot because they accept guns at their package stores and are gun friendly. UPS is a little rough on packages.
Pack your boxes well.