Welcome to ChefTalk!
I have to admit that, off the top of my head, I don't know the cutlery availability in New Zealand, or the import restrictions and duty of cutlery or accessories into New Zealand or if there is any VAT in New Zealand, so take what I have to say with a grain of salt and verify anything I have to say.
I am first noting the New Zealand to U.S. dollar exchange rate (1 NZ$ = 0.84 US$) and the U.S. Dollar to New Zealand exchange rate (1 US$ = $1.19 NZ$). Since you did not specify which currency, I am assuming your budget is in New Zealand dollars, which means you are looking for individual knives in the (U.S. dollar) value of up to $84 to $168 range. If you were using the U.S. dollar as your currency value comparison, then $100 to $200 in U.S. dollars would work out to $119 NZ to $238 NZ.
I'm glad to read where you are willing to forgo buying a set and will buy your knives individually. As many of the people on this web site will advise (and as I am now doing), you don't need all that many knives. A good chef's knife, a moderate quality paring knife and a serrated edge bread knife will form the basic cutting edges of your kit. You will also need a good cutting surface and a honing rod right away as well, and in due course, a sharpening kit.
The basic tool will be your chef's knife. This is the one knife for which you will need to be willing to open your wallet. Everything else can be lower level, but your chef's knife requires some expenditure.
The first question you need to ask yourself is - how long do you want the blade to be? One expert on this site, Boar de Laze ("BDL") (who now seems to have gone to other pursuits) saw a 200 to 210 mm blade as small, a 240 to 270 mm long blade as moderate in length and anything longer (300 mm plus) as a very long knife. You need to chose the length according to (1) what is comfortable to you now, (2) what you can grow into; and (3) how much food can you reasonably expect to work with in the vast bulk of your food preparation sessions. My personal experience as a rank amateur is that I started with a 210 mm blade, and then found that a 240 mm blade was comfortable after a short mental and experience adjustment period. I found a 270 mm blade to be just too unwieldly. However, that is me - you might have a different experience.
After that, you will be looking at availability. In terms of a New Zealand retailer, you might want to consider ProChef.co.nz, who are based in Whangarei. They are the New Zealand authorized dealers for MAC knives (which is how I located them). They also sell, Tojiro, Masakage, Sakai Takayuki, Yoshikane, Akifusa and Sakon knives.
The MAC Professional has been cited by BDL as among the best stainless steel chef's knives for a basic gyuto. I recently acquired one and can recommend it. While ProChef does not list the 240 mm Mac Pro MBK-95, they do show a 220 mm MAC Pro (presumably the 210 mm MBK-85, along with a ceramic honing rod and a 125 mm paring knife - presumably the PKF-50) as part of a "basic" kit for NZ $319.00. However, as the New Zealand importer/distributor, they can probably special order the MBK-95 if it is not part of that kit.
Both the Tojiro DP and the Sakai Takayuki are well-regarded gyutos (though I am not particularly a fan of a damascus style blade. I think they are an affectation, with owners potentially being afraid of using them and causing visual - though not functional - damage to the face of the blade. But that's just my personal quibble). As for the other Japanese gyutos from ProChef.co.nz, I don't at this time have any real information.
If it works for you, a MAC Pro 125 mm paring knife would make a nice petty - though so would a 150 mm. Or, you can follow BDL's paring knife recommendation and just get some Victorinox paring knives. Much cheaper and a lot less critical than the chef's knife.
For a bread knife, go for a basic Victorinox fibrox handle serrated bread knife (at least 8 inches - 200 mm, but preferably 10 inch - 250 mm or longer) as a good, inexpensive and reliable bread knife. The ultimate bread knife might have been recommended by BDL as the 10-1/2 inch (270 mm) MAC Superior bread knife, but ProChef does not seem to stock it. You might go whole hog and ask for it as a special order, though that will cost you.
The MAC 240 mm honing rod is good for knives up to 240 mm in length (though I would probably prefer something longer - such as 300 mm, like the 12 inch Idahone available in the US). But in any event. look for a ceramic rod, rather than anything made with steel.
As for a cutting board, there's plenty of advice on ChefTalk about cutting boards (including mine). Have a go at the archives about that, though I suspect that the shipping costs will be disportionately high for large heavy objects to New Zealand and significantly affect the budget for a good board.
As for a sharpening system, I have two suggestions. First, consider several Japanese water stones, at least 210 mm in length and 50 mm wide (but bigger is better). You should get at least a 1000 grit stone, and something in the 3000 to 4000 range as well. ProChef does offer a Tojiro combo stone which would at least initially work well. Then, go online and read this:
This is a short version of Chad Ward's 2006 book, An Edge In The Kitchen. I don't know if the book is available in the New Zealand library system, but you might want to see if it is and then if you can borrow it. Prices are hopelessly out of date, but the information is sound.
There are plenty of videos online as well. Look at Jon Broida at Japanese Knife Imports. Bob Kramer and Murray Carter are two American-based Master Bladesmiths who also have some interesting online videos. Chef Knives To Go also has sharpening videos.
If you want to go a guided sharpening system, my personal recommendation is to look overseas to the United States and to Chef Knives to Go and look at the custom Edge Pro Essentials kit being offered for less than $250 US. It's the Edge Pro Apex sharpening system, but with custom stones (Shapton Glass). This site's administrator (Nicko) got me to do a review.
If you want to look at buying online from overseas, there are a number of knife retailers on line who can and do export to New Zealand. The aforementioned http://japanesechefsknife.com/ is well regarded. And as I mentioned earlier, an American web retailer who ships internationally is Chef Knives To Go ( http://www.chefknivestogo.com/ ).
Hope that helps.
Edited by Galley Swiller - 8/24/14 at 4:31pm