Cleaning the roof stains will make a big difference. Read up about algae on the roof, this may be what you have.

I'd likely paint the front door to match the shutters and the porch floor like or a shade darker than the siding.

Black is good with beige siding, but you have a dark brown roof. Not sure about that combination.

Congratulations on your new home. I think this house would look good without all the shutters. With the window grilles, porch railing & lattice it's busy looking. The porch floor may be a composite so I wouldn't paint it. Beef up the columns. Update the landscaping. Paint the door black

Are you going to replace or washer pressure roof?

Watch out for pressure washing an asphalt shingle roof. It can damage the shingles. There are other methods.

Remove the decor, clean the roof and post new pix with a close up of the porch floor too. I think the house will look better without the shutters, but if the siding has faded, you may not want to remove them. The house would be a lot brighter, especially under the porch, if the shutters were white. Rethink the conical shrubs. Can they march up a driveway?