Looking for suggestions for which Network is best for what I want.
Why not drop MMS and use one of the many IP-based messaging apps that allow you to send media?
Linux: Only one carrier in NZ offers Wi-Fi calling and that is 2degrees and it's a fantastic service
if you look for wifi calling. 2d is the only choice.
binijo123: Have a look at Kogan Mobile, their plans seems to be working similar to Skinny Direct. New Zealand MMS is also covered in their plans as per their website. Haven’t tried it yet.
Yes free MMS as part of the deal and free access to voicemail and unlimited talk and texts on every plan.