A current pic showing the green roof would help. Based on the pic you posted, I would say black for the door, too. Depending on the roof color, a green that blends could also be nice for the door and shutters.

I like black too

Charming house!

Here’s an example of black, it looks good … but as chloebud said, we really need to see the current roof. If you could get a pic similar to what you posted in your op, more mock-ups could be done.

A pic showing the style of your front door would be helpful, too. What color is it currently? And are you planning to paint the storm door, or leave it white?

Another option is red, to complement the brick.

I did red and orange examples, but don’t know how they’d look with a green roof. I couldn’t find the exact red I wanted to show, this one below is a bit bright … maybe someone can show a darker one.

I would paint the shutters a similar green to the new roof, and then pick a warm color for the door, such as a soft orange or a medium toned wood stain.

What difference does the door color make when it's behind a storm door? Don't bother. Spend the time and money on landscaping where it will make a difference.

“…but don’t know how they’d look with a green roof.”

Jilly, that was my thought, too. Just wondering how green the roof is.🤷‍♀️