Savannah (SAV) is about 45 minutes from Hilton Head and probably your best bet if you are traveling international. Hilton head airport (HHH) is the closest and easiest if you can find a flight here.
I would absolutely rent a car at the airport once you arrive.
I would either rent a house or apartment on vrbo. The closest area to our house and the wedding venue is Seapines or north /south Forest Beach. But Hilton head island is only 12 miles long so anywhere on the island should be fine .