I think you're making the right choice in picking specific areas rather than doing Te Araroa, although it's improved NZ isn't really that good for thru-hiking.
My favorite area of the country by some margin is Mt Aspiring National Park + Fiordland (they border each other so really it's a continuous area), which is also the largest single park area in the country. I spent nearly 2 years hiking about 12 days every month in this region, and haven't come close to covering even the main routes through the area. Pick up a copy of the two Moir's guides and you have a huge choice of trips, I can give you a list of some of my favorites if you like, on many you might not see a single person for days on end even in summer. If I only had a few months I'm not sure I'd bother with anything in the North Island, Stuart Island gives you a good taste of what the low level bush walking in the North Island is like. One issue you'll find is access to the trailheads, ideally you'd buy a cheap car and resell at the end of your trip. Organising trips with resupply is pretty hard, impossible in the best areas without something like a helicopter drop, so this naturally limits the length of single trips. Though you could stash supplies at or near the trailhead/roadend and loop back before heading out in a different direction.
The sandflies in summer down south can be pretty overwhelming, and they can bite you through a head net where it contacts your skin. They generally disappear not long after dark, but this can be late when the days are long in December, even when you walk 12+ hours a day you're still going to be faced with the problem. At least the bites don't itch badly though. I got through two summers ok with just a bivy and a tarp, but this time around I will go for some sort of inner net or tent, I'd strongly consider this. It can be pretty hard to camp high to avoid them even if the weather looks ok, often you just won't have the option.
Expect rain all year around, there isn't a wet or dry season. I've used Goretex, Event and now a cheap Marmot Mica jacket, and noticed no real difference between them, I'm sure your anorak would work just fine. Plan on getting completely saturated, so have enough clothing for the day that you'll be warm enough when you're soaked through and walking in the wind and rain at near freezing temperatures, even in mid summer. Often this means you might feel you're taking too much gear when the weather stays mild for a trip, but the weather can vary immensely, it can snow on the higher routes in the summer On the brightside it means I'm generally taking a very similar kit for most trips which keeps things simple. Take some rain pants. Apologies if this paragraph comes across as at all patronizing : )
Outside of winter I was ok with a 16.5oz Nunatak Ghost + 6oz hooded Nunatak Skaha Vest, in a bivy bag. Again, it felt like too much at lower altitudes on warm summery nights, at other times in cold wet weather higher up I really needed it all. Don't be stingy with your pad R value, sometimes you'll be on stony and wet ground which will sap your warmth. Although usually you can, don't rely on wearing any day clothes, they may be too wet and I can tell you from bitter experience drying them in the bag won't work.
One of the great things about NZ is that you can do a lot of walking all year around. My personal favorite is spring, because there is still snow on some the mountains, the days are long enough for plenty of walking ,the evenings/mornings are cold enough to keep sandflies away, and the whole place is less busy than summer. However, practically late summer/autumn can be the best time for some of the hikes involving some of the high passes because they are more certain to be clear of snow, and my impression is that the weather is more settled in late summer/autumn (I haven't checked the stats though). And as soon as you get off the popular routes you really don't see anyone all year around anyway. Winter is a good time for the lower altitude walking, but the days can get a bit short (take a book!), and it's a bit uncomfortable pulling on frozen shoes in the morning and crossing painfully cold streams. But unless you're really getting high (ie with crampons and an ice axe), it doesnt get cold enough to warrant any real winter gear like waterproof shoes, just a warmer bag, thicker pad, and some extra fleece during the day. Often in winter you'll have some of the big 40+ bunk huts to yourself.
Aside from the long route around Stuart Island I would avoid the great walks in the busy season unless you are an absolute novice hiker with no tent (which you are not). The tracks are very flat and groomed, there are large (40+ bunks) huts filled to capacity every night, and you need to book huts and often even campsites, some which are expensive and which the annual hut pass won't cover. Don't get me wrong, they do cover some fantastic areas, and they are a great idea for people just getting into walking or who might not otherwise get outside. But there are plenty of other routes which are just as good or better with fewer people and better for camping. There are some offtrail routes which you can include parts of the great walk tracks of some of them anyway.
Let me know if you have any more questions.. Also http://www.nztopomaps.com/ is great for planning trips, you might even be able to get usable prints from this and then get them laminated (paper maps can be disastrous, you really need to be able to read maps in the rain).