There are 2 main networks in NZ - Spark and Vodafone - they both issue SIM cards themselves plus Telecom has a "budget" brand called Skinny which uses Telecom's network. There is a smaller player called 2 Degrees which has a limited network but also uses Vodafone's network.
Of the 2 networks Spark's / Skinnies is much better. For example, I live within 20 min drive of downtown Wellington- in a suburb - and Vodafone has very little coverage here - Telecom is perfect. This is not an uncommon example. The hills make NZ pretty -but they make building a network HARD!
Spark/ Skinny coverage is pretty good now on the road network - all state highways have cover I believe - might not include data though. Notorious black spots for any type of coverage include East Cape, The Forgotten Highway (in Tarnacki - highly recommended) - most places around the Taranaki coast outside of towns. The west coast in general outside of towns.
You can buy SIMS pretty much anywhere - supermarkets, corner stores, on arrival in airports (probably don't know what has reopened in Auckland airport ) .
The rates you should be paying are here https://www.skinny.co.nz/pricing/plans - they do have a special "travel SIM" but it seems to have limited availability. As a tourist there are no restrictions in buying a normal SIM $2 from memory - putting it in your phone - added your credit card and buying a plan (or paying as you go - but that's a lot more $$$) If you don't want to add a card I think you can still buy pre-paid vouchers to top up - but I'm not sure how available they are as NZ is very much a card rather than cash economy.
If you are hiking in the SI you are unlikely to have any cell coverage - if you get any consider it a bonus- don't rely on it. The hiking group should have an EPERB or satellite phone to call in an emergency.
If you want a card in advance and you're not arriving for a few weeks - I'm happy to drop one in the mail for you - message me your address. If you have it with you - you can probably put it in your phone and activate between the flight landing and you being allowed off!