It you did a porch in the same style as the one in your inspiration photo, used some bigger windows, or instead of 2 smaller windows have 1 larger one, and get rid of the side door, that should make it look more cohesive, however it would be wise to extend the porch a bit past the indent created by the addition to make it appear as though it was always there. Once more creating a cohesive, traditional look.

That makes a lot of sense! Thanks!

I think adding a rounded portico like the one below to the front of the house would go a long ways in helping it have a more polished and finished look. It will also allow you to keep all the natural light flowing into those beautiful windows. The round shape will also contrast well with the strong lines of the house and add more dimension.

For the picture window, I wouldn't necessarily get rid of it, but rather it would complement the style of the house if it was a large paned window and could be very beautiful there.

If you set aside the issues with the newer addition for the moment and look at the old part of the house compared to your inspiration photo, you will note that your front door is smaller than the window above it. In the inspiration pix the door is also smaller than the window above but the addition of glass side lights and transom light give the impression of more volume and therefore more importance.

If it was my house, I would duplicate the inspiration picture exactly and then run a raised patio at the same level across the window to the right on the old house continuing the length of the addition. Instead of a covered porch on that side, I would consider a pergola.

Is the house historic, or just old?

I don't have an answer but your house is beautiful!

Here is what I notice:

Look at the distance between windows comparing your house to the inspiration. Your house is much more compact. I think the full porch would be out of scale on your house. I think a portico would be more apt.

I am not bothered by the secondary door. Do you actually not use it? If so I guess you could remove it.

For quick big impact, paint the storm door to match the interior door, and a solid glass one would improve the look too. You really only have space for a portico to give shelter to the stoop. I think a pair of more primitive style lanterns that have a candle style lights would be more appropriate. Can you remove the lattice at the porch and add more stone to the sides of the stoop? Apply the same principles at the side entry, and replace the picture window with a pair of windows to match the ones on the rest of the home. Its looking great!