We have been to Northern Finland a few times during the winter and have managed to capture the lights a couple of times (it can be cloudy during December).
This was a useful read:
I have a very old DLSR (Olympus e450) and although it is quite old fashioned by today’s standards it can still take decent pics and something of that vintage can be picked up for next to nothing.
As everyone above has said, a tripod is a must (I have tried a monopod but they are a waste of time for long exposures).
The lights can look pretty unimpressive to the naked eye but the long exposure photo will bring them out. If you are unsure if you are seeing the lights and not just clouds try taking a pic and see what they look like.
I am not sure what the temperature will be like but if it is very cold, take spare batteries and keep them close to the body (we were seeing -30 Deg C at times).
The image below was taken with a 20 second exposure time.