1. Registered mail is for items with intrinsic value. The item is signed into and out of each station and Registered Mail moves in separate bags and is stored in separate secure locations. But, passports have no intrinsic value (besides their replacement cost), so Registered Mail is of no use, takes longer and costs a lot.

2. As between the rest, any will do. USPS Express or Priority or any of the overnight carriers.

But, as others note, make certain that the Consulate with which you are dealing accepts deliveries for this purpose via the method you are considering.