As far as I'm aware, no college deliberately tries to pick more public/private, they just go for the best people who apply. The reason that some colleges have higher rates of public school/private school pupils, generally speaking, is because more public school/private school individuals applied to that particular college.
That said, Jesus is 58% state school, Pembroke is 44% state school, and Christchurch is 47% state school, as an average between 2005-2007, so it looks like Jesus would be your best bet if you want state school company, or Pembroke if you want private school company.