I see Leumas has sent you a PM, which should be of help as he has done exactly the same thing as you are about to do.
AX cards are accepted at all major stores [Gas Stations, Supermarkets, et cetera] and some other independent stores. It goes without saying to get a VI or IK card aswell. A good secondary credit card for NZ rewards would be BNZ VI PLT or a card from the Westpac Lineup [The VI/IK cards in the GlobalPlus Lineup aren't as good as the Westpac ones]. For QF, ANZ do a card much like GlobalPlus.
Depending on what rewards you take from your card, the AX PLT credit card might be worth it - IIRC 'tis only $325 pa. If you want to earn Air NZ Airbucks you can earn them very quickly with the Gold GlobalPlus AX.