If you buy me a ticket to come along, I'll let you use my gear for free!
But if you insist on renting, I'd really suggest a 14 mm of some variety. When you are that far north, the aurora comes in right over your head and is all around you. So the wider the angle, the better. I did okay with my 14 f/2.8 prime in Yellowknife (see below). For this one I only needed a 3 second exposure at ISO 2000, but granted it was a pretty good show that night so the aurora was brighter than average. The downside to a UWA lens is the keystoning as you tilt upwards (notice the trees are angled inwards). But in Iceland you don't have trees to worry about so this effect should be less noticeable.
Have a great trip!