Norway does not have one best month. I grew up there, and the answer I give people depends on what they want. Snow, a swim, or the midnight sun. Pick that first. Then pick the month.
Summer, if you want the easy version
June, July, and August give you long days, open roads, and ferries that run. In the north the sun barely sets. That is the Norway most people picture. It is also the busiest. Cabins go first, and the famous viewpoints fill up by late morning. If Geiranger or Lofoten is on your list, book the bed before you book the flight.
September is the month I recommend most
The tour buses thin out. The mountains are still green. You can walk without standing in a queue for the photo. The evenings get dark again, so bring a warmer layer than you packed in July. I would rather have a quiet fjord in September than a perfect July day spent looking for a parking spot.
Winter, if you actually want winter
January to March is when I tell people to come for snow. December is pretty, and the days are very short. February is the month I prefer. You still have snow, and the light is coming back. The cold is the part that ruins the trip if you guess. I wrote what to pack for a winter trip to Norway for that reason. Read it before you buy another thin coat.
Do not try to see the whole country
Norway is long. One week is one region. In summer, pair a city with one fjord. In winter, stay put. I would not drive a long icy road just to tick a place off a list.
If the trip is mainly for photos, start with my 4 best Instagram spots in Norway. Then match the month to the place. Trolltunga is a summer hike. Hamnøy is the one I would save for the low winter light.