D600 or D800, Rockinon/Samyang/Bower 14/2.8 or 24/1.4, Nikon 14-24, Zeiss 15/2.8 or 21/2.8. You'll most likely want to shoot WIDE ...
I'd avoid the highly corrected faster f/1.4 lenses if you want nice star points across the frame because they tend to be affected by coma. That would include the Nikon 24/1.4 for example.
Exposure with Aurora is dependent upon the 'look' of the image. Shorter exposures will have more shape and detail. Longer exposures will tend towards the more diffuse Aurora look. I'd start at something like ISO 1250/1600 or so and shoot at f/2.8 focused at infinity (true infinity as found on your live view of a star - not necessarily the end of the focus on the lens!). Time will depend upon the conditions but < 20s.
The main thing is that you want a good exposure based on the histogram and the 'look' of the image. Noise can be cleaned up but is very controllable on the D600/D800 or similar full frame cameras. You could use other lower resolution low noise options such as the D3/D3s/D700 or D4 etc too. Newer typically is cleaner.
There are some good web sites out there about night photography that will also cover shooting the Aurora Borealis. Generally speaking good night photography technique will also apply to shooting the Northern Lights. Trust the histogram and not the LCD.