I'd say base the decision on the child. Home schooling is going to give them more individual attention, so if a lack of social interaction with peers during school hours doesn't outweigh the benefits of the one-on-one-ness, then go for it. Public schools do introduce students to a wider diversity of cultures and ideas (usually), but don't have the resources nor "expertise" of private schools. I went to public school and was happy with the experience, but that's just me.
As for college, all I can say is this: base your decision on what campus, student body, and style of classes suits your interest. Ranking should be one of the last considerations you take into account.