Freebird, you can only go as far south as Christchurch on a train so that's the place to pick up your camper van. There is the Overlander train from Auckland to Wellington, then you'd have catch a ferry over Cook Strait to Picton and then there is the Coastal Pacific train from Picton to Christchurch. The trains only run once a day each so somewhere you will have to stay a night either in Wellington or Picton.
With the price of airfares being so competitive these days you may well prefer to just fly quickly to Christchurch and get on with your tour.
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