I'm also heading out there: in less than 2 weeks now ( time to start seriously thinking about packing :-)
The Pedaller's paradise books seem to be out of print at the moment. I have the South book from a previous trip, and agree it's better than the Lonely Planet book. The PP timings assume your fit and on a reasonably light touring bike - so make allowances if otherwise.
Also check out this link
http://www.cycletour.co.nz/
As your bike experience is limited you really need a friend (e.g fellow cyclist from your backpackers/YHA ) to check bikes and kit before you buy. A second hand 26" hard-tail MTB without suspension is possibly your best budget bet (might even come with a rear pannier rack ). You will also need some basic tools and a helmet ( by law in NZ ).
It would also help, i.e. quality wise you would get a better distance bike, if you plan to buy and then resell the bike at the end of the trip.
Another option is to hire e.g.
http://www.bicyclerentals.co.nz/bikes_touring.html
Also most resorts hire MTBs so you could try hiring one for a few days running around once you get to each location.
As Valygrl said, the busses are excellent, and are the way most backpackers get around.