I did exactly that in 1993! I second the suggestions to check out the area first before you decide. I agree, it's easier to fit in in a larger town then a smaller one. Also be aware of the cultural differences. You may have to deal with blue laws, parking laws, and assorted other things you would never think of in NJ. Be prepared for lots of questions about your religion. In NJ most folks are usually Catholic or Jewish, in SC those are two of the least common religions. Again, this is in the smaller, more rural areas. I lived in the upstate in a rural area where there was 1 Catholic church within 20 miles and it shared a priest with the next closest one.
The schools, in the area I was teaching/living in, don't quite follow the seperation of church and school rules. We had teachers encouraging students to pray, principals who brought their paster in to do a Christmas program, and prayers at snack and lunch time. Not saying that all schools do this, just the ones I was familiar with, or even that it's a bad thing, just that it's different from NJ.
There is a lot less local control of schools in SC. The state sets the kindergarten cut off date for all schools at Sept 1. In the upstate most of the schools started at 8 am, then the older kids got out before the younger ones in the afternoon. School lunches are about half the price as they are in NJ. If your child doesn't go to public school they usually don't bus to private schools like the do up north.
The biggest surprise is the car tax. You pay personal property tax on your car every yr. While the insurance is MUCH cheaper in SC, that tax can be quite a surprise if you own a newer car. It's a percentage of the value of your vehicle but I can't remember the % rate. Home property taxes are also much, much cheaper because the schools are not funded by it. I think those are the biggest differences.