Just be yourself! They are looking for someone who knows their subject, can teach it and can contribute to the school environment - much like the state sector. The school you went to should not influence the outcome of the interview, your enthusiasm will be more important. Beware though that staff often play a fuller role in the pupils' day in independent schools. You may have break & lunch duty, evening music activities from time to time, Saturday & weekday evening 'open days', interviewing applicants, marking entrance papers, lunch time clubs...... Check the website to see what the school gets up to and if you get shown round the school, look out for the notice board that may give an indication of what is going on.