Try a mid-century modern rug like Hemphill's Rex Ray Area Rug Collection or Jaipur Traverse Caracas. I looked up 'mid-century modern rug' and chanced upon these on Houzz. I like the muted colours which would soften the cream on brown. The mid-century motifs would highlight the mid-century chair. Good luck!

Sounds like you have a lot of white in your home! Do you have any interior/exterior images of the spaces in mind? It may be easier to get feedback if we know what we're commenting on. Sometimes a picture tells a thousand words!

Suggestions from neutral colours: https://www.dulux.com.au/colour/colour-trends/2018/essential Ceiling & walls the same colour is a good choice for square set. There will be subtle hue difference in various lighting situations anyway, which provides depth and makes for an interesting look.

With such a large house I think it would need some other darker colour along with white to help "ground" the look. Also, as mentioned above, pure white on an exterior looks very glarey - surfmist would be perfect. I would strongly suggest getting a colour consultant to help with such a large project - and get some mock-ups done with different colour ideas.