The wall color would be the last thing we will select (most of the time)
Why? There are thousands of paint color choices to choose from, but way less choices for upholstery, rugs, tile counter top etc, so it's easier to match a paint color to all the elements in a room then vice versa. It's much harder to commit to a wall color first and then look for a sofa, chair, window treatments, tiles or counter tops that will match that wall color.
It's important to understand that usually, the wall color juxtaposes or "touches" everything in the room: the flooring, furniture, window treatments etc. If that color clashes with any of these elements, it will be noticeable.
So basically, once everything in a room has been selected, I pick out a color that will work with all these elements.
What if you can't find a color that will work perfectly with all the elements in a room?
That's when you need to prioritize, and decide what is more important and what is less.
Proximity - anything that is in close proximity to the wall color, like window treatments, back splash tile, sofa, cabinetry is more important then what's "floating" in the room (a chair, table, small rug).
Size - the large items like your sofa, window treatments, large rug, wall tile, floor tile etc. will have more impact on the overall look of the room then the small items.
The off white (Ben Moore linen white 912) wall color relates to the rug and serves as a backdrop to everything else in this room (designed by Vered Rosen)
The exception to the rule - when to choose color first
When the wall color is the major design statement in a room, that's when you want to pick it first, or at least have a few options which you will revisit as the other components are selected.
For example, in this teenage girls bedroom, I selected a bright blue, which is what this girl really wanted. It had to work with the existing carpet, but pretty much everything else in the room was selected after it was painted.
Last, although I usually recommend to leave the final choice of paint color to last, I will always consider which color family will work best, and make sure my clients are happy with this direction.