Re: gun laws, this is a good site worth becoming more familiar with: http://www.nraila.org/GunLaws/Federal/Read.aspx?id=74
That said, SC welcomes you and your firearms! No need for permits or FFL involvement unless you want to conceal carry (I know nothing of NFA rules, be forewarned). If you want to have a Concealed Weapons Permit (CWP in SC) contact SLED and a concealed weapons permit instructor.
One request--please don't move here and vote to make it "just like back home"