I did 3 journeys into North of Norway, two by car. Northern lights I experienced in September 2016 on Lofoten.
VisitNorway has a map of locations recommended for Northern lights. Best to reach by plane are Tromso and Narvik (EVE).
As travel time I recommend dates around new moon.
Finding history will be a challenge in parts of that area because in WWII Germans burned down all towns of state Finnmark (storched earth) when they left the area - Kirkenes is a sad example for that. Only the main church was left.
You will find some things around Sami culture. And also Alta's rock carvings are a journey into the past. On Lofoten you will find a Viking museum. The Hurtigruten museum in Stokmarknes tells a lot of establishing the supply line along coast of Norway.
Stave churches are more located south of Trondheim. Trondheim is not on the list for Norttern Lights (too much south) but has a fantastic Cathedral.
What you could think of: Fly to Trondheim, stay there 1-2 days. Embark a Hurtiguten ship (port-to-port, online booking in Norwegian only) and enjoy a nice cruise along the coast into the north (trains end in Bodo, so will not help). Your desitnation port can be Tromso or Honningsvag (close to North Cape). From there you could take a bus back to Tromso.
If you are open for car round trip affecting budget I have further ideas.
Hope that helps at the first steps.