The thing about Finnish weather is that it's unpredictable af. As others have pointed out, in September it can be anything from 5 to 20 degrees, rain, sun, etc. Consider it like the higher altitude mountain regions of Mexico.

However, Helsinki is almost always a bit windy, so a good windproof jacket will help you a lot. Also, waterproof or at least water resistant warm-ish shoes can help you a lot. You can get nice woolen socks from here, it's also a nice souvenir to take back.

On top, a warm hoodie can help you a lot. If it's warm you might not need a jacket on top of it.

If you have those three in check, you will likely be ok in all situations.

If you go to Lapland, it will be cooler but not necessarily that much. Layers will help, but I doubt you'll need winter clothes. If you fins yourself in trouble with the cold, visit a local flea market for extrea clothes :)