hi there.
not to dampen your enthusiasm but maybe have a look thru old posts here in regards to claims and all the legal wrangles involved with such in NZ. while nz is a great country and very scenic you might find getting a claim in your own country easier. anything is possible with money and lots of time though.
perhaps if you simply just want to come to nz for its beauty and a chance to get outdoors you could try the public areas(there are a few but hand tools only), or try and hook up with someone already with a claim.
you could buy an existing claim. there are some on this site
www.trademe.co.nz. just beware that some people create "claims" that may not even contain profitable gold, i.e.. they may have done no testing. simply selling as an investment in tying up resources really.
there are lots of places to prospect over. you could create you own claim but for this you will need to allow a lot of time.
i find it hard being in nz figuring out all the rules and who wants what money off you to get started. i know of a local claim that took forever to get paperwork sorted and they spent thousands and can't even use a dredge. apparently they are handtools only and can't even move rocks?! so beware. best bet is talk to as many miners as you can first.
hope that helps some.