I think all white will be a very nice scheme and the differences in the white will just add subtle difference. In the above pic the walls are more white than the table, but mixing with the light tan colours and greyish tones makes this gradient of whitish tones work well.This room is all white as well with the furniture and walls, but adding the punch of the other colours masks if the whites are slightly different as the bright colours become the focus.

The walls in the pic below 'read' a very pale grey so that would be an option, just ensure that it is a whitish-grey and not muddy or warm.

I would choose the sofa colour as your main colour and accents to match from there.