I usually take 3/8 bubble wrap to start with, then take Kraft heavy paper and try to square off the rifle. I take measurements and have a heavy cardboard box make. Shipping out of state required the proper paperwork inside the package, and I usually put a copy on the outside in a shipping pouch.
If it's a rifle I really want to protect, I buy a cheap plastic rifle case from Academy. I have a heavy cardboard box to fit the case and fill the voids with heavy kraft paper. I put cardboard square in the case to keep it from collapsing, usually in the middle somewhere. So far, no problems. On expensive stocks, I wrap them with 3/8 bubble wrap, put it in a round cardboard tube, then stuff it in a square box tightly fit.
I go overboard, but it's cheaper in the long run. Filing an insurance claim is a pain, and worse, you beautiful piece of art you spent several months on is gone. For those reasons, I stay safe.
I usually start with the USPS, then UPS, then FedEx. USPS, well I personally have good luck with them. I can say the same for UPS as well.
Build the package and make sure it survives a 5ft fall to concrete. Drop it on the ends, sides, flat, etc., you get the point. They all tend to throw packages around when loading.