I am using ANZ, and I will provide you in detail on how I got my first bank account in New Zealand.
Just present your passport and visa to any nearest ANZ branch in your place and the banker will assist you with opening your account. After providing all the details, instantly they will give you your EFTPOS card which you can use every day for buying to grocery stores, topping up your ATHOP (bus and train card), or in retail stores.
With ANZ, I have two cards, one is my EFTPOS card and the other one is visa debit card. I received my Visa debit card through mail about one week after I applied for ANZ account. In the meantime, you can only use your EFTPOS while waiting for your visa debit card.
It is very easy to transfer money from visa debit card to your EFTPOS card, just log on to ANZ website with your customer ID (the banker will give you the information for that) and you can quickly transfer your money from there.
It is safer to use your EFTPOS all the time, so when you lose the card, it only has your money for daily use. Anyway, it is also easy to block the card when you lose it, in my case, I lost it in a grocery store, and I called the ANZ customer service hotline, they quickly blocked the card and sent me a new card through the mail in just three business days.
By the way, remember to tell the banker (if you want) to cancel automatic deduction for your EFTPOS card when it has zero balance. Because what happened to me is that, I was not able to check my balance with EFTPOS card for a long time and I continuously use it, (I didn’t know it’s already negative), so the bank penalized me and increased my interest rate because I only paid the deduction maybe a week after. So, I went to the bank and asked that to the banker, Lucky me because the banker is really nice, she just canceled the penalty and stopped automatic deduction for my EFTPOS card.