The majority of whites will have a yellow or orange tone. The yellow will be more visible when you use warm white bulbs with a Color Temperature below 3500K. Most incandescent bulbs are 2700K. Florescent and LED bulbs are available in the full range, though you might have to shop a specialty lighting store to find neutral color bulbs in the 4000K range. Warm white is relaxing and kind to skin tones; cool or daylight white is great for detail work, but is harsh on skin tones. HERE is how a room looks under various color temperature lighting.

I will suggest Sherwin-Williams SW 6007 Smart White as a neutral with a red tone. It's on the window wall and the wall left of the fireplace.

HI -- I have currently fallen in love with Sherwin Williams " Greek Villa ". Just get a small sample to try in your space .

I second that SW Greek villa is pretty- I prefer it to the ever so popular SW alabaster that I find goes very yellowish sometimes. that said, i ha e had Greek villa myself and it can go yellowish.. and sometimes it does not. Depends on the light. SW Snowbound is also very pretty in certain lights and another color you could sample.

Look at this color. Very neutral.

Color of the Year 2016 - Simply White - Setting for Four · More Info