Having once owning a Postal/USP & Fax shipping business I learned the importance of packing well & if the item is valuable ship by Priority to reduce handling & damage.
Over the past 3-4 years due to advance age & need to downsize I've shipped numerous antique firearms by USPO Priority & insured & knock on wood no damage problems with any.
Tips;
Try to find a suitable length long gun box at a gun store or buy one from a shipper, can often run $30.00 or so for a heavy duty double sleeve box.
-If shipping a long rifle in a home built cardboard box line the inside with thin wood paneling & outside edges with small dia. pvc pipe or wood trim.
Smooth off any sharp wood edges & use lots of packing tape to protect all corners & edges.
-Better yet, construct a box from thin wood paneling edged with 1"x 4" trim , put rifle in a soft case, fill interior with padding & use small sheetrock screws to seal up.
-Never throw away a Kibler rifle box