Have a look at Sherwin Williams “Sea Salt” for your green.

We’ve painted several rooms that color and it always works.

Another vote for Sea Salt. Our master bed and bath, and a friend’s whole first floor.

"Antique White"

The floor are unstained oak, red oak I think. With oil finish, so it has yellowed.

Furniture is unknown. The bigger room was an exercise room, so no future worth mentioning.

I'll take a look at some of these.

Is Sea Salt a gray? It is reading gray for me.

No, it’s a beachy blue green. Reacts really well to natural light.

I think it's impossible to help you with only using a computer screen, as the color looks different on different screens, and will definitely not look the same on your wall. Plus what works great in one person's home will not work in another person's home, due to differences in quality of light, taste, and furnishings/finishes.

If your floors are warm, you need colors that won't clash with that.

Here is my method--and I always get lots of compliments on the colors from visitors:

Narrow down in your mind the family of color you are interested in (in your case blues and greens).

Go to several paint stores and get every single paint chip they have in that color family that has the approximate value/intensity you want. It doesn't matter which stores/brands they are. Any paint company can custom mix any color for you. If the color you end up liking isn't offered by Benjamin Moore, take them the chip and they'll copy it. (Personally I prefer the quality of Sherwin Williams, fyi).

Take the paint chips home and attach every single one to a wall in the room, using white artist's tape or a sliver of masking tape. If the walls already have a strong color, put each chip on a piece of white paper before haning it on the wall. (or even better, put down a layer of primer before you begin.) Separate the chips from each other enough that you can look at them individually without getting the others in your field of vision if you narrow your focus.

Now just leave the chips there. Live with them.

Pretty much right away you'll see some you absolutely don't want. Take them down.

Every time you walk into the room, eliminate a few more that just aren't doing it for you. Look at them in different lighting, at different times of day.

I look at the chip colors by squinting my eyes and then visualizing the color spread over the whole room. And if there is furniture or there are other design elements I want the color to work with, I have those close by so I can look from one to the other. It takes a little practice to see the whole room in a color from just looking at a chip, but you can do it.

Keep on with your process of elimination. When you are down to four colors, you can pair them off: "this one? or this one?" Keep eliminating down to two. Then get small samples made up of those two colors and paint the colors on the wall in 2'x2' sections--not close to each other. Again, live with it for a while.

When you are sure of your color--get the custom mix done. Or if it happens to be a standard BM offering, you are all set.

Bear in mind that flat will look different from eggshell which will look different from glossy.