Our 4 boys attended public and private schools. One even attended a boarding school. If we had to do it over again, we would home school. We had friends that home schooled their kids and there was no problem with socialization. The local home school organization had regular get togethers. Also between church youth groups, youth sports, scouting and countless other activieties you can put a child in, I don't see how you couldn't have your child get the social exposure you want for them.
Charter schools and on-line schools didn't really exist when our kids were in school. I would have to look at them. I would consider a good charter school where the focus of the program (and the rules) was a good education for the kids.