Maybe a seafoam color its a nice tan color but not the usual apartment tan or white. I had it before along with a nice red carpet in my bedroom and it made it look like I had more space.
I would go with a soft, dove gray, with a silver hue in it. It won't clash with the red. If you prefer to go dark like your furniture is...& to expand what the space looks & feels like, then try using a deep shade of brown, if the room isn't too small to handle it. You can always paint an accent wall in a lighter color. Possibly a shade of that silver I spoke about. Then use accents in the room of other color. Possibly an aqua shade, or even purple. Lay out samples of each color on a table in your room, & see how they appeal to you together before you slop any real paint on the walls. Then you'll know how it's going to turn out for you. Good Luck !!
You could use wallpaper that was both red and dark brown.....
A shade of beige
Tan, orange, Earth green - I am thinking of a tan for my room. It has brown furniture and a red carpet like yours.
Pink carnation from home depot
A very very light yellow
The usage of light color like off-white or cream color suits best with furniture and carpet so you can use this to your room for paint so that you get it in right way.
I think a reddish color would be neat. But I would have to visualize it first before I could tell you anything. Just picture it in your mind and think what you think would look best