First, the colors can be divided into warm and cool colors. The Warm colors red through yellow including browns and tans. The cool colors are blue green through blue, mostly grays included.
The warm and cool are relative. Depend on the texture; any color can be made into warm or cool color.
Depend on your taste, if you like mysterious and dull environment, you would like pick the colors within same color system. For example, you can use burgundy, dark brown, and taupe for your burgundy furniture room. If you want a vivid, layered color structure, you would like picking different color such as gold, beige, sage or sky blue.