Do you have a specific question or two.

I'd remove the canopy but otherwise I don't see the problem. When I see your house this is not an area that stands out as needing work.

My wife and I both dislike the main entry / mudroom. But while we are at it... what would some suggestions be for the home? I took some better photos and the green storm door will be painted white. We live in CT so paint on the brick is out unless a very light white wash, however then you have the chimney to match too.
I would love a porch to hide the overhang, but it's not in the budget. I have debated on some sort of roof over the front door that is sized to the stairs.
I would welcome any ideas to make the house look great!

Is the arched wood structural? If not, I would remove it completely and just paint the rest the same white as the house. If it is, I would square it out so it's even across the top and paint it all white. The storm door would look better replaced with a full lite door. I would remove the shutters from the brick portion of the house since they are too small to fit the windows properly. You could add a pretty painted bench to the left of the door for some color. A canopy like this over the door would be easy to install.

I would also add some color in with your hostas-astilbe or daylilies are low maintenance. Paint the storm door the same color as the front door to make the door appear larger. You could also paint your downspouts so they blend in with your brick.