I agree with the above posts- staying at lots of DOC camps is the cheapest way to see the place. Small fees, though only certain camps are patrolled. This method does require renting or buying a car/van to live out of. Vans are nice, as lots of the bugs on the south island are horrendous. If you search around, one can typically find an outfitted van off someone trying to leave the country. Prices can be super cheap. Make sure it is still current with all it's paperwork- they need to have inspections every 6 months or so and they take this seriously.
As far as camping gear (and the smaller items of boating gear)- SHIP ALL OF IT THERE! The gear is ridiculously expensive in Kiwi land. Not sure about prices to rent stuff since I shipped it there or purchased it while there.
The Hokitika area has some absolutely amazing boating on the south island (21ft of rain a year), though most of it is in the class V realm. There is some good boating on the north island, though I much preferred the south island.