I would do whatever you want on the inside, but I would paint everything on the outside White.

Prime first with a high adhesive primer (water base) like KILZ® or BIN and paint the exterior of the door, sidelights, and all the wood a semi gloss exterior white. The storm door and the interior door will look like one big door. Clean and fresh.

SW Naval is a bright navy, but too dark for a door that gets sunlight, it will fade fast, and get hot and peel.

change out the light fixtures and replace your house numbers for a refresh.

Good point about the heat- the door faces east and it gets quite a bit of sun.

I live in Canada we use good quality steel doors no strorm door and if a screen is wanted I use Phantom So IMO find a ggod quality steel door in a color from the factory .

It's hard to see what the style of your home is but my guess is sort of a Colonial. The front door and sidelights don't really match that style. So, would suggest your replace with a style that does.

You could try painting the white storm door and matching storm window frames with a medium brown that is a close match to the wood door color. Try the brown paint samples on small scraps of trim board before painting the storm door. The wood door and its flanking side lites are beautiful as they are.

I would leave it wood like it is. It looks to be in great shape. I am happy to hear you are leaving the storm door. I would never live in a house without storm doors. If they were not there when I bought the house, they would be there before I moved in. I love having the dead bolt lock on storm doors these days, and also the pull down screens some have, since my doors are all opened to those storm doors when I get up in the morning and they dont close until I go to bed at night, unless, I have to be gone from the house. I do have claustrophobia, which is probably one reason why those doors have to be open all day long.