Camera Body: Almost any camera―either digital or film―will work for photographing the aurora, as long as you can adjust it manually to take time exposures of 10-30 seconds or longer. An all-automatic camera may not work well for these photos, I'm afraid, but it's certainly worth trying.
Digital cameras do a great job if you set them for a fast ISO (800, 1600 or faster). Cold temperatures will sap battery strength, so carry spare batteries in a warm place, such as an inside pocket, an change them out from time to time. And don't worry about using a light meter; it usually will only work for your daytime photos!
For shooting film, an older mechanical camera body―one that doesn't use batteries to open the shutter―will usually work best. That doesn't mean that your automatic or semi-automatic camera won't work. Always carry plenty of spare batteries.
[Dennis' Equipment: Currently I use a Nikon D750 DSLR camera body for shooting the lights.]
[Dennis' Recommendation: Any camera that can be adjusted for manual exposures. For film, a mechanical, all-manual camera body is best; many digital cameras also work well.]