I'm not a designer by any stretch, but just painted my home. Previously had a neutral main color with accent walls, bedrooms and bathrooms different colors. I did the entire home in Sherwin-Williams Silverplate and kept Dunn-Edwards Swiss Coffee for ceilings, trim and baseboards. I love it. The color looks lighter/darker given different light conditions in each room. I have white shaker cabinets and gray quartz counter. I think it would tie in to the gray in your counters.

I suggest you ask the same question on the Home Decorating forum. From what I have read there, this is not the best way to choose wall color. They always say pick the rug and furniture first.

On the other hand I suspect you want a color so neutral that it will go with anything you choose later. Just like Mxzm9, I am also not a color expert. I do know that BenjamanMoore colors Revere Pewter and Edcomb Gray are very popular lately.

I would have the living room and dining room all the same color.

Sherwin Williams has books that put together colors that look good together for adjoining rooms.

I've been toying with the idea of choosing just 1 color and then getting it one shade darker and 1 shade lighter to make 3 colors.

That's harder than you think it would be. Two problems with that color strategy:

1. Remember that most strips of paint color chips are NOT 'color strings' or in other words, all one color, just different lightness/darkness values on the strip. The majority of paint color strips are comprised of DIFFERENT colors. A few brand's color strips are strings, but not many.
2. When most people try the all one color, just different values color strategy, it ends up you can't tell the difference. When it's done, it all looks like one color. To pull off different values of one color, there has to be pretty big leaps in terms of contrast from one color to the next - leaps that are not for the color timid.

Considering your circumstances, I'd suggest you get a swatch of Mushroom from Ellen Kennon Full Spectrum Paints. It's super flexible color with the potential to shift and morph harmoniously as you add pieces and change things going forward.

Just wanted to update you guys (I know it's been a long time!)

Thank you all for the suggestions. I ended up going with 3 different shades of the same color for the hallway, living and dining room. I should have jumped a couple of shades darker between each instead of one because the living and dining room colors at times look the same.

I ended up with navy blue (gasp) in the kitchen which I love!