Either white or gray. Both would look good.

I would not rely on computer color representation to make your decision or to get others' opinions, as every monitor shows color differently. I have my monitor calibrated for professional graphic design work, and yet their copper penny color sample looks dingy pink. Copper has many color overtones, highlights and shadows and varies so much according to daylight vs. indoor light, time of day and surrounding colors. For starters, see if you can get an actual sample. Second look at photos of copper, both interior and exterior (Houzz is a good place). (These, too, are not exact replicas of actual color -- you're looking for general ideas.) Once you've narrowed your colors down a bit, get some large color swatches and see what looks good in your light and with the surrounding environment. For example, mossy green is usually a good companion with copper, but if you are surrounded by greenery, this may not be the best shade. Are you out in the sun or shaded by a grove of trees? In addition to house style, consider your context. A metal roof often suggests a country setting, but is that true or are you on a city lot or in a development with houses close by? When you have it narrowed down your choices, post a photo of your copper and large paint swatches here to get opinions. (Note: the colors will still look different from reality, but hopefully they will be altered to a similar degree.) When you have three contenders, paint large areas on several sides of your house, preferably at the corner where you can see surrounding trees and neighbor houses.

The window trim change would be to Craftsman style. Unless you are doing the work yourself it seems a lot of expense for little difference on upstairs windows. It would, however, be extremely easy to do on your front door as you would only need to change the top board. And you could replace the side lights with solid wood inserts, or you could use textured glass that would obscure the view while still letting light in. While the limestone exterior is very light it has a yellow hue. Simply speaking the easiest way to find colors that work with the warm limestone is to choose a nearby color. That was probably why the trim is green. Since you prefer a modern look, I suggest you keep your siding light and use color only in the trim. Below are two combinations that I like. I darkened the roof color in these pictures.

@Jon Alan - this is a custom house that we are about to pour the foundation for so the structure is pretty much set at this point. (Thanks for checking first - LOL!) To clarify, the inspiration house was inspiration for colors more than shape/structure. (The inspiration house is in an area prone to flooding which ours is not and we wanted to keep it lower.) As far as a black/gray brick, we really like the warmth of the redder tones and haven't cared for other homes we've seen with black/gray brick so I don't see us going that route.