I always say if you have to a new, sturdy (double walled if possible) well fitting box with added padding if needed is best. I lost an insurance claim on a car seat shipped in the original box for "insufficient packaging" once because it was the second use- turns out the box strength rating is not guaranteed after the first use as crumpling may already have occurred.
Of course first choice is not to check it- in order the first choice is use on plane, then have someone buy on the other end or order to have waiting, then arrange to buy when there, then ship ahead insured, THEN check protected are my preferences.