Kia Ora – good to be set up! There is no legal requirement to have a bank account for your Company, albeit if you want to trade then you will likely need an account. So not required underlaw but if you want to make payments and receive payments, it will be needed.
In terms of which banks – they are very vanilla in their offers, and what you are looking for is a bank that has a startup package or an offering that is light on fees. I have personally banked with BNZ and ASB recently, but I have also looked at KiwiBank and I have thought about TSB and other local banks.
If you want to email me at @manaaki.io">firstname.lastname@example.org with a little bit about you, I can do an intro to KiwiBank and BNZ if you like as I know people there?