...here I searched for 'Living Room gray walls brown furniture'. It gives me ideas I wouldn't have come up with on my own.

https://www.google.com/search?q=living+room+gray+walls+brown+furniture&oq=living+room+gray+walls+brown&aqs=chrome.0.0j69i57j0l6.8491j0j9&sourceid=chrome&ie=UTF-8|

a photo of your room and "paint" it with any color you choose so you can see how it looks. For example: https://www.sherwin-williams.com/visualizer#/active/scenes

..my latest is the Behr paint color..Glitter...it is in the gray family of colors..but interestingly enough, the color depends on the light of day..sometimes looks like mauve, sometimes, blue, but mostly a very warm gray..this is 1 bedroom and attached bath..(even though the color name is glitter, it does not glitter, it changes color ever so slightly with the light of day)..

to arrive at the chosen color..I taped sample colors on the wall for a couple days..

https://www.behr.com/consumer/ColorDetailView/N540-2

May I also say, always use ceiling flat paint on a ceiling..have fun..

I go to Home Depot and grab a bunch of color cards/booklets and take them home. I pick my favorite 4 and go back to HD and get a sample of each. Then get a sheet of poster board and cut it into quarters. Paint each quarter with one of the samples. When all of them are dry tape them to the wall. It’s a big enough sample you can really get a feel for how the room will look. Then play elimination. Last one taped to the wall is the winner. I save a piece from the poster board I end up using. I take it with me when I go shopping for stuff for that room. I’ve painted every room in my house a different color and that system hasn’t let me down.

For ceilings I always use HD bright white eggshell. I detest flat paint because it’s impossible to clean.

Sometimes the light will change how a color will drastically if it is seem in a different location.

Another thing that can change how colors look is the color temperature of the lighting. With incandecents it used to be you'd only have a couple of choices and Soft White was the way to go. Now with LED lights you can select from 2700k to 5000k, sometimes on the same fixture. A few of the ones I've looked at have WiFi control to adjust the temperature of the light emitted!

There a 6 major types of color schemes, and many other subsets. You can combine any colors any way you'd like, but so some color combinations are just better than others. These major color schemes utilize colors at certain locations on the color wheel, so start with your favorite color or the dominate color in your existing room.

Start by looking at the 6 major types of color schemes and find one that appeals to your taste and style. This will eliminate a lot of the guess work about what colors work together.

Thanks, procon. I googled and here's one of the first links that describes the 6 color schemes: https://learn.g2.com/color-schemes
And here's the couch I'm looking at:
https://www.la-z-boy.com/p/sofas/leighton-sofa/_/R-610653
with the color B166302 or C124191 (one can use the search button, next to "All Patterns" on the right, to bring up the couch in those colors)
I read online that the loveseat should be the same color as the sofa, and a nearby chair should be a different color to provide an interesting complement or contrast. Discovering the right color for that chair as well as for an area rug that pulls all this seating together is my goal right now.

I get those paper samples for the store. Tape them onto a wall. Several times a day I look at it and x out the colors. After a few days, I move the location and start the process again. After a week, I'm usually down to a few choices.

My current favorite color is Favorite tan by Sherwin williams, in a flat. Go into a SW and try to get one of the paper samples with that on it.

Grays are a tricky color, it can look blue in sunlight.

You and others here have responded with ideas to help find a wall color, and this has got me thinking I should include that investigation and discovery as part of my overall design task.

Is what direction the natural light comes from that lights the room. If light is from the north paint colors will appear cooler, slightly bluish, so if that is the case and you have a choice of two colors you may like, say two taupes and you want a warmer look to the room they you would look at what colors are added to the paint. For example, if there are warm colors added red or yellow it will look warmer than a taupe with blue added to it. Conversely if light is coming from the south it will make a room appear warmer. If you want to cool the look of the room choose a paint with cool colors added to it. This is why large paint chips are a good idea to make sure you like the color in the room.

I once painted a room in a pale yellow, loved the color, finished the room. Everything looked great. Then I went in the room at night with the lamps and ceiling light on, it showed as a horrible yellowish grey. Ruined the whole look of the room. Lesson learned. Had to repaint the room.