In preparation for this build, I did some research on the body color of the Star Destroyer. In their first appearance in Star Wars: A New Hope, they were pretty clearly white (and again in Rogue One: A Star Wars Story), but in the other films, they look more gray. However, apparently that's a trick of lighting and the huge ships are indeed white. The studio models were white. I didn't want to just paint the model white, though, as I was afraid it wouldn't look detailed enough or "real" enough. So after priming all the pieces, I started with a coat of light gray. Then, I airbrushed white over the gray, but only did a light coat, which results in a more textured finish with subtle variations over the hull that give more of an impression of it being a large vessel.
I started these photos after having painted the hull and after starting to assemble some pieces. The most time-consuming part of this build will be drilling tiny window holes into the hull.
Last update: 2/12/2019
The inside of the main top hull piece (this was actually two pieces). Light blocked.
Exterior surface of the top hull piece.
Bottom main hull.
Leaving this section open from the front to install lighting...
I drilled a hole here to run wiring up through the "tower"...