You need someone with a Federal Firearms Licence on both ends to ship it.

Traveling with the rifle is no problem. Read the regulations for the airline you are flying and the TSA website. Process is pretty simple the security folks take a peek in your presence to make sure its not loaded, no ammo, and the case is locked where nobody but you can get in. I traveled with a handgun this summer not really a problem. Then it just rides in the bottom of the plane.

Check the South Carolina laws for weapons transport because some states require the firearm be in a case while in transport. Michigan is like that where it has to be in a closed soft or hardcase while in transport in a motor vehicle.