Lake Te Anau is beautiful. We took the boat trip to the glow worm caves and I got some lovely shots while on the lake.
Milford Sound is fantastic, I recommend taking the overnight cruise because most of the scenery is, I believe, only visible from a ship. The cruise itself is fun, too, you might see penguins and seals. The drive to Milford Sound it itself quite gorgeous, be prepared to stop often!
Lake Wanaka itself presents some nice, if ordinary vistas.
If you can get to the Franz Joseph glacier, do it! If you can take their helicopter hike, do it!
If at all possible, take the ferry from the south to the north island. Queen Charlotte Sound offers many lovely scenes.
If you will be Auckland, make every effort to get to Tiritiri Matangi. It's a large island that has been converted to a nature preserve devoted to the native New Zealand flora and fauna, with foreign "visitors" actively removed. The island itself is gorgeous, hilly with many steep cliffs at the shore and all sorts of unusual plants. You might be lucky to see some uncommon birds, too. The boat ride to the island is also full of interesting scenes.
When I went, I had a Nikon DX-format camera, the 18-135mm Nikon kit lens, and a 10-20mm Sigma zoom. These served me very well. I try to strike a balance between having every lens I might want and having a kit that is easy to carry and deal with. Vacations are to enjoy, not to spend lugging and fighting with photo gear.
You'll have a blast - and I wish I could go back!