Insulation, Radiant and Vapor Barriers - Old house, renovating, no insulation

This old house was built in 1959. It will definitely need to have insulation blown in the attic. We are in South Carolina. The wiring is next on the list and have found there is zero insulation in the walls. Some walls have had to come down due to the renovation and we are thinking about taking the remaining exterior walls down to insulate. Question, is this the best alternative and if so should we cover it with a vapor barrier? Also, how important is it to insulate the crawl space? What types of roll insulation, should we use for the walls and the crawl space? Should it have paper backing and which direction should the paper be facing for the wall and the crawl space? Thanks in advance.

There are plenty of ways to reinsulate a home. I'm only going to comment on the vapor barrier requirement:

Take the time to look up 2003 International Residential Code Section R318.1 Exception 1; it states that most of the counties in South Carolina are exempted from requiring an interior vapor barrier. The code is effectively washing its hands of any moisture problems that arise from installing an interior vapor retarder in this climate.

But is it warm enough to support an exterior vapor retarder, like in Florida? I wouldn't say that.

I would look to installing one of the insulation systems that can eliminate the need for a vapor barrier. Cover your bases.