The main problem with fibre is that it's unavailable in some areas of NZ. It also requires an installation process that warrants a technician's visit. Another thing to consider is that fibre connections tend to be more expensive than wireless or copper ones.
However, on a tight budget, you can check out NZ's cheapest unlimited broadband plans for Kiwis. You can also opt for no-contract broadband plans, which are a smaller financial commitment.
You can try several other plans if you don't have access to fibre broadband options. For example, you can try satellite internet like the infamous SpaceX Starlink broadband plan.
Rural broadband connections and landline internet plans are also provided by internet powerhouses such as Sky, 2degrees, and Slingshot.