Such vibrant colors! Love it! I would vote a neutral to act as a backdrop. What color is your trim, or do you plan to paint that also?
I would paint the trim also. We rent and have crummy popcorn ceilings so that will probably remain white.
would go with a neutral also and a shade lighter or darker for the trim - gloss trim
We have a light, neutral tan color on most of our living room walls, and it sounds like the same might go well in yours. It is a Sherwin-Williams tone called Macadamia. You can use a color visualizer on the S-W site to see if you like this color in your room if you upload photos of your room. You can also go lighter and darker in the same color family. S-W lists a whole array of related colors for each color you pick.
I am seeing "Greige" a neutral color with a bit of beige and grey!
I think keeping the color you have now and paint the wall behind your couch in a turquoise as an accent wall would look really nice. You just need a das of color. You can even do two walls if you see you need more color. Either two walls together or across from each other.