I plan to start a new job in PA. I am considering my rent (or buy as second home) a place in NJ that is convenient for my wife to work and son to go to top school. Should I consider buy a house in PA (as primary home) close to my work so that I am a PA resident, save income taxes and property taxes. Would this work? Is this tax efficient? What is requirement in terms of spending time in PA? If I spent most of the day working in PA then does it matter how many days I sleep in PA house?

Your resident state is determined by where you sleep at night the most. So determine how many nights/year you expect to spend in PA and in NJ, and that will tell you which state you would be a resident of. PA does tend to have lower taxes than NJ, so yes, this sounds like a good way to save taxes. You'll have to determine whether the added costs of maintaining a second home makes it worthwhile.