Here is the way I got around the South and the highlights of my southern Kiwi adventure.
I decided to keep my backpacker roots alive and took a Kiwi Experience bus around NZ. I was only one of two Australians on the bus (the other being my travel buddy) so I found it quite refreshing to meet plenty of different nationalities - made lots of great friends and had plenty of interesting conversations. There is another backpacker bus called Stray and that takes a similar route to the Kiwi bus as I saw it around plenty of places where I stopped. Many backpackers on the bus had recently been to Oz or were heading there, so I had plenty of stories.
Other options include taking your own wheels or flying around, but you will still need to drive to get to some of the smaller towns without airports. Driving might have saved me from the terrible motion sickness I got on the windy roads on the bus. Thank heaven for motion sickness tablets.
Another fun tip: The South Island is full of one-way bridges (one of which is even shared with a train!) and windy clifftop roads all around the island, so make sure you're not getting distracted by all of the beauty around you.
You'll probably be flying into Christchurch or Queenstown in the South. Or Wellington in the North Island and then you can catch the ferry down to the South. The backpacker buses stop at all the major cities including those three above, the Abel Tasman National Park, the West Coast, Wanaka and the southern cities of Dunedin and Invercargill. I found that two weeks was plenty of time to do the traditional South Island route on Kiwi, but they let you stop anywhere they list along the map, meaning there's plenty of national parks and other towns where you can enjoy getting to know.
I extended the traditional Kiwi Experience route by staying two days in the Abel Tasman National Park (definitely worth two days) to walk and kayak for longer than a few hours, then longer for NYE in Queenstown (which also deserves two or more days). Otherwise I found sticking to the Kiwi route perfect. If you're driving, the freedom is all yours, but you will end up driving in a particular route along with all the rest of the travellers as the Southern Alps mean there's only so many ways you can go.
My favourite places along the route was Kaikoura, a little coastal town north of Christchurch which is a hotspot for marine life, the Abel Tasman National Park, Fiordland National Park (which is the largest of NZ's national parks full of the stunning fiords of Milford Sound and Doubtful Sound), and Queenstown.
NZ is not the cheapest holiday you will ever take. You have to pay for the beautiful experience. Being an Aussie, the New Zealand Dollar actually saved me a slight bit of money in the exchange rate, but for two weeks backpacking on the bus, staying in hostels, eating, drinking and doing activities, I easily spent over $1500NZD, not including my flights from Australia, which due to it being Christmas, were expensive. They would be more pricey from Europe or the US over the holidays and you might have to fly via Sydney.
As I like dining out, I could have capped my expenses down more by cooking in hostels, but I budgeted for eating and drinking. Getting a guide/reading one in your hostel will help you find the cheaper places to eat, but some of the smaller towns, such as Franz Josef and Kaikoura, don't have as many eating options to choose from so cooking might be your best bet to save money.
A dorm bed is usually around $30NZD standard. Just to give you an idea of the high season pricing change, in Queenstown around NYE a dorm bed was $55NZD. Doubles will usually be around $70-$80NZD in a hostel. Accommodation will always be a stickler. That is where camping would be a great option to save money if you've got a car/bicycle.
The Kiwi Experience bus pass I got, including my add-on of accommodation and a Milford Sound day trip, was just over $1400NZD. Again that was travelling over NZ's high season. Right now (January 2016) the prices look to be around $700-$800NZD for the trip I did (and other similar trips), and that will change again with sales and holidays. I ended up getting a lot of activities and accommodation cheaper due to being on the bus, so that is definitely an advantage if you're travelling in a holiday period. Just make sure you get all of your vouchers for anything additional you buy on the backpacker buses. I was not sent our accommodation vouchers via email and I ended up not getting refunded for the additional money I paid at one of the hostels... That was partly my fault for not checking everything was sent to me before I started my holiday. Think I would have learned that after so much travelling! Car rentals depend on the type of car/campervan you get and where you stay, but remember NZ is quite a journey from the rest of the world so petrol is pretty pricey.
NZ also lives up to its 'adventurous' nature by having a plethora of activities you can do: Bungy jumping, bungy swinging, glacier hiking, kayaking, scenic flights, canyon swinging, skydiving, paragliding, parasailing, jetboating, canoyning... They all will cost you over $100NZD. Anything involving a helicopter or plane is easily looking above the $300NZD mark. So unless seeing or jumping off as many high things as possible is your aim, pick your adrenaline rush activity or two and stick to it.
One of the choices I made was "The Ledge" bungy swing from Queenstown's Skyline. Bungy swinging from "The Ledge" was $160NZD. You can get discounts for a second jump or doing another jump at another one of their jumping locations. "The Ledge" swing in Queenstown was the scariest thing I've ever done (before that it had been jumping off a ledge while canyoning in Dalat, Vietnam - I'm not one for intense 'thrills' obviously!) but I would do it again.
If you can afford to do more activities NZ has stringent safety procedures and is a great place to jump off things. But your price doesn't always include transport there and will most likely not include the photos/videos/shirt/other merchandise of your experience. Just remember to factor in the additional prices of things before you book five different activities to do. AJ Hackett Bungy (who run the bungy's in Queenstown) give you a free hat/t-shirt and certificate after your jump if you can live without a photo.
I also did a fast jetboat ride in Queenstown for $125NZD, which included transport to and from the boat, but not any photos/videos (and you can't take your cameras on the boat). Kayaking I did twice while in NZ and both experiences cost me around the $100NZD mark. As above, any major activity is going to cost you over $100NZD plus anything extra on top of that you want to buy, so just prepare yourself for that.
Although you have to pay for those thrills, sitting on a beach/lakefront is always a great free option (if you can handle the chilly water). Frisbee golf in Queenstown's gardens is also free and tramping around the South Island numerous walks won't cost you anything.