When you arrive you will probably set your telephone line up with Telecom; N Z's version of B T. They offer different broadband packages from 1GB at quite a slow speed, through to 10GB. Visit www.telecom.co.nz
and look for a link to their 'xtra' page.
Also, as you are a techno geek the same as we are, mobile phones... Vodafone have sim cards, Telecom don't. That's it - no other choices. If you aren't on Vodafone but plan to bring your UK mobile, make sure you get it 'unlocked' by your present provider as it's hard to get done here unless you know the right (or should that be wrong?) people
Only then can you get it to work on the above two networks. Also, forget trying to send picture messages via your mobile from a N Z network. Stick to the digicam and send them via email.
Hope all that helps.