Start with the things you are not changing: sofa fabric, floor tone, fireplace stone, curtains, trim, and large rugs. The wallpaper should connect to at least one of these elements, even if the link is only a shared undertone.
Warm oak floors usually sit well with cream, clay, olive, ochre, tobacco, or warm grey backgrounds. Cooler floors and black metal details can handle blue-grey, charcoal, cool white, sage, or mineral tones. Avoid choosing living room wallpaper from a screen alone. A background that looks soft online can read yellow, pink, or icy once it is beside your real furniture.