First, have a look at how the deck appears presently.
Here's my current thinking: The 16-foot posts will be the color of the siding...Benjamin Moore's Timber Wolf (gray). The railings and pickets will be the color of the cottage's trim "Chantilly Lace" (white). The picture below shows the gray siding and white trim colors.
The ceiling is tongue and groove with those exposed beams. Do we paint, stain, or use a semi-transparent stain? Should the beams be the same color as the tongue and groove or a shade or so darker? Blue ceiling, white ceiling, natural wood look ceiling, or gray ceiling? Pale or bold ceiling? IF we go with blue, here's the shade I'm leaning towards--Sherwin Williams "Atmospheric".