I don't understand your comment about casement and awnings as both are available with screens (on the interior). Over a kitchen sink, I do not like double hungs especially if one is short of stature. They are difficult to reach over a sink. Casements or sliders are a better choice. Marvin also makes Integrity which is fiberglass exterior / wood interior if Marvin is out of your budget. Take a look at them since you have spoken to a Marvin person.

Something to think about: If you go with the 6 x 6 window, and want it to open and not cost too much, it will probably have to be a sliding window with a vertical mullion up the middle. Or you could get fancy and more expensive with a fixed pane in the middle and single or double hung integrated windows on the sides. You didn't mention if you are getting wood, aluminum, or vinyl windows. If you go with the two 3 x 6 windows, they can be single or double hung with a horizontal mullion. A lot will depend on the style of your house.

Well, jmho of course...but I think that drapes should look like they could close, even if they won't. So I vote for the long rod and full drapes...so they would need to be sheer or semi-sheer to get the volume.

If the window is a little drafty curtains would help. I wouldn't do a plain white though since your walls are white and the furnishings are gray, white and black. A mid-tone of almost any color would work, or just some sort of pattern with a white or gray background would perk up the space. Hang them as Lyn Nielson recommended. It looks like the window is not too large so a standard off the rack size should work (two 50" X 84" panels).