2 Degrees Mobile is generally the cheapest option. (Vodafone and Spark, formerly Telecom NZ, are the other options and they are generally much of a muchness - although Telecom operates on different frequencies, so make sure your working before you walk away from the store)
There is a Whitcoulls in the International terminal where you can buy a 2Degrees SIM.
Website is here: 2degrees - 2degrees Mobile
You can see all the plans etc available there also.
You have a few options for internet
but the simplest is just to include it with your mobile plan and use that. All the networks will offer you a USB dongle if you're that way inclined.
There's free Wifi
around the place in typical cafes etc...