I would check out your online banking facility before you leave for adding overseas accounts. With my bank, it took a little bit of time to get it set up, just had to get codes to do it properly etc. Then when you get to NZ, you can just add your NZ bank account as soon as it's set up and start transferring.
Always when I am going overseas, whether to live or just for short trips, I always call and notify my bank and the credit card companies so that they don't freeze your cards. It's a good idea to call them as soon as you have a contact number in NZ as well, so they can easily reach you if they need to check any suspected fraudulent transactions on your accounts.
Hope that helps!