Just make sure that the details you've taken care of include this. I believe the form is a 4457 form, and while it only proves to US Customs that the rifle had any import duties and applicable federal sales tax (Pittman Robertson, etc.) paid on it, it is viewed as proof of leagal ownership by other countries. You will have trouble without it.

If you have it (can't hurt for scopes and binos, camera too), relax and enjoy the anticipation.

Best of luck,

JPK