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Hate to break it to you, but you simply cannot afford an i7 on that budget. Plus, if you're going to be gaming I'd recommend a lighter processor and a heavier GPU. The i5 750 is right up your alley. It's a mainstream i7 equivalent and it's quad core. It's also $100 USD cheaper, uses cheaper motherboards, and also only uses dual channel RAM (as opposed to triple channel on the i7). It's a downgrade, sure, but you'll still be getting a lot of performance from the i5.

Intel Core i5-750 Lynnfield 2.66GHz 8MB L3 Cache LGA 1156 95W Quad-Core Processor BX80605I5750
http://www.newegg.com/Product/Product.as...-_-Product
$199.99 USD

Pick any of these motherboards. You'll find their prices are much more reasonable and they'll likely be easier to find in NZ. I'm going to budget $150 here for a mobo.

http://www.newegg.com/Product/ProductLis...20(LGA1156)

The case I find is a personal venture, and I have no idea what cases will be available to you, so I feel a bit finnicky about telling you which one to get. Just make sure it has front intakes and rear outtakes and you'll be fine. The CPU itself comes with a stock cooler that will be able to OC a little bit for you. Budgeting $100 for the case.

As for the RAM, I am partial to my own RAM:

G.SKILL 4GB (2 x 2GB) 240-Pin DDR2 SDRAM DDR2 667 (PC2 5300) Dual Channel Kit Desktop Memory Model F2-5300CL4D-4GBPQ
http://www.newegg.com/Product/Product.as...-_-Product
$85

For the Power Supply, it's hard to go wrong with Seasonic:

SeaSonic M12II 520 Bronze 520W ATX12V V2.3 / EPS 12V V2.91 SLI Ready 80 PLUS BRONZE Certified Modular Active PFC Power Supply
http://www.newegg.com/Product/Product.as...-_-Product
$80

For the video card, I'd recommend the nVidia 460 GTX 768 MB. It costs maybe $10 more than a 5770 and is a lot stronger. It should be easy to find in NZ too as it's not exactly a brand new part.

MSI N460GTX Cyclone 768D5/OC GeForce GTX 460 (Fermi) 768MB 192-bit GDDR5 PCI Express 2.0 x16 HDCP Ready SLI Support Video Card
http://www.newegg.com/Product/Product.as...-_-Product
$169.99

And then you also need a hard drive:

Western Digital Caviar Blue WD5000AAKS 500GB 7200 RPM SATA 3.0Gb/s 3.5" Internal Hard Drive -Bare Drive
http://www.newegg.com/Product/Product.as...-_-Product
$55

And a CD-ROM Drive

LITE-ON Black 24X DVD+R 8X DVD+RW 12X DVD+R DL 24X DVD-R 6X DVD-RW 12X DVD-RAM 16X DVD-ROM 48X CD-R 32X CD-RW 48X CD-ROM 2MB Cache SATA 24X DVD Writer LightScribe Support
http://www.newegg.com/Product/Product.as...-_-Product
$25

Add that all up and it totals $865 which is under your $1000 budget. Can you see how there's really no way you can fit an i7 in there without cramping your video card?