I believe most of the large consulting firms in New Zealand run graduate programs (at least their Australian counter-parts do). I would suggest you apply through those.
I actually am in my final year and am to start at Deloitte next year. I recommend them as people that remember that you're a person and not just a statistic or a number. Of all the firms I applied to, they showed the most consideration for the applicants.
What these firms usually look for is a background/history of leadership and teamwork, and also a life outside of uni. It's not about your marks, so much as about how well you will fit into their culture.
Good luck.
-Nelson