I am also from NZ been in Thailand 15 years Apply for what is "called" a retirement visa from the zthai embassy in Wellington Web site is good explains it all but u need apart from passports
1 Police report get from NN justice depart on line application no issue but takes a few weeks
2 Medical form signed by your GP suggest get first form done but not dated GP will advise Then in future just copy last form and date.
3 Financial info from bank or eg.Milford finance showing available funds
4 If you have friends or family in Thailand Intro letter from them like s character ref.
5 Ticket to Thailand can be just itinery re travel doesn't have to be paid for at application time
The visa section in WLG very helpful they will respond with advice and info via e mail..Fee is around 300$/person and visa from embassy is always multi entry unlike when applying in Thailand thru an agent when it cost 4000b extra for multi entry.
Or just use a agent in Thailand at a cost of about
*****
b which includes opening a Thai bank account.