I'm really liking the Capitol White. I think it would look really good in the living/dining area. Here is one picture of some sample boards. Not really large enough to show context, but it works with the space. My concern is I think it might not play nice with the color in the kitchen. Truth be told, I'm not in love with the kitchen color but I don't want to repaint. I've uploaded a photo of the sample boards in the kitchen. Last picture of downstairs bedroom. The plan would be whatever color is in the living room/dining area would flow up the stairwell. So I'd like the new color to play nice with bedroom color. I think it does. Finishing the stairwell massive painting project is next, and then I can get the flooring all put in and be done with the downstairs. I also have sampled out a few other whites too, but will save those for later.

Are you saying light comes from the north until late in the day, or are you saying there is a window facing north and a window facing west.? The reason I ask is that light that enters from a north-facing window is bluer and lacks intensity. Subtle color is washed out to gray. The Inchyra Blue is very dark, looking more charcoal with a green tone to me. I would choose the Cooks Blue. Here is a comparison I put together of those two colors with some blues from your rug.While the actual colors may be off due to how color can vary from monitor to monitor Cooks Blue is brighter and won't fade as much in northern light. Also, having a brighter blue on the walls should bring out the blue in your rug. The only way to know how it looks in your room is to buy a sample and paint a board as you did for other colors. Keep in mind that the color temperature of light bulbs you use will also affect the colors of your walls and furnishings. Color Temperature is expressed as Kelvin but is not a measure of heat. Warm-white bulbs have a color temp of 2700K which is kind to skin tones but gives a yellow light. Daylight bulbs have color temperature of 5000K to 6500K, but are harsh to skin tones and emit a blue-white light. Both CFL and LED bulbs come in various color temperatures. I recommend you choose bulbs with color temperature between 3500K and 4500K for a more neutral result. HERE is a photo of how different K-value lighting affects the appearance of color. You might have to visit a lighting store or light bulb specialty store to find neutral white bulbs. As to ceiling colors, people seldom look up. Unless your light fixtures are dramatic or the ceiling color is distinct I doubt anyone will notice if two adjacent rooms have different ceiling colors as long as there is a Framed Passageway between them.

Please clarify this statement... "I like more war, colors like the beige or light tan to coordinate with each other." Also it is hard to recommend colors without some idea of the space and how the rooms relate to each other. Do you have a floor plan, sketch or pictures that you can post to help us give you ideas? Whole house open concept or 3 separate rooms with doors or clearly defined separations for different colors of paint. Also what color & type of flooring, furniture, cabinets, rugs, art etc... Without any of the above I can say I like the following colors & you might start your paint journey with:

And once you get your items in the space, you will see what the colors really look like with your lighting. Trying to find a gray that works is the subject of many., many posts on Houzz. I would recommend an in-home color consultation. With all that light, you should be able to do some fun accent walls (maybe a cool wallpaper behind the entertainment center). The key to making in homey are the plants, textures, and larger-scale knick-knacks. The thing to keep in mind is the dark wood floor you will have. You will want to choose rugs that bring the light down onto your floor.