Navy base wood doors.
Or White base would both look good.

Do you have a recommended navy paint colour ?

There are too many colors on there, and you have gray stone, and gray roof. I would look for a nice lighter shade of gray. Pick a gray from your stone. It isnt cohesive right now, with different color browns and tans. Without being able to see the exact stone, it is hard to pick a color of gray on a computer monitor, since all monitors are a bit different. I would not paint the door, nor pick a color for the door, until the house is repainted. A brighter color on the door, would show off your entry area, much better, than what you have.