Long-term housing starts at about $250 a week for a furnished two bedroom house. It can go up to $500 a week or more for seaside or multiple bedrooms. Don't rent a vacation home from New Zealand for very long since long term rentals are so much cheaper. You cannot find long-term rentals until you get here. Look in the newspaper and ask people around you.
I am from America, not New Zealand. I don't know what you're used to, but there are so many things and brands you cannot get here, so bring extra of anything you would find in a pharmacy.