Ammo and mags go in your checked bags. Trust me. You wont be taking them in your carry on bags.

You are limited to 11 pounds of ammo. It has to do with the net explosive weight (primers) in the ammo. They dont care if its 50 BMG or 22 LR. Put the ammo in original packaging. It isnt 100% mandatory, but it makes life easier.

Get a good hard-side case to ship your rifle in. Consider pulling the bolt to make it easier to verify it is unloaded. Ticket agents are not gun people and can get twitchy when you start racking the bolt back and forth to show them it is unloaded.