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Whatever you use it will invariably suck in some way. PX is fine, but getting a merchant account sure isn't. All the stripe clones in NZ are balls. Please, Stripe, whatever you're doing to get to NZ, double it!
Using Paypal at the moment, as te_chris said PX pay is decent but requires a merchant account which is expensive and slow to setup. As far as I am aware their aren't any other decent solutions. Kiwipay could be good but at the moment it isn't really suitable for anything more than casual payments.
Aside from merchant account setup, last time I looked (4 years ago), Payment Express worked out to be really expensive when charging in USD. I think it was in part due to merchant account/currency conversion charges by the bank. It was significantly more expensive than Paypal. I don't know if the situation has changed since then.
I know that the only bank that allows international currency transactions is BNZ so they are likely fairly expensive seen as they have an monopoly on it.
Technically (for those who don't know) they allow multiple currency transactions from one/single account. So you may have 1,000 NZD but it's made out of USD, PHP, AUD etc