Are the colors primaries— in which case I’d go with cool white, or muted which might lead me to ivory / warm white. Enjoy doing this project together!

The ivory/beige coloring of the large-print floral and the flecked squares is the largest color block, so I would work on coordinating with those. But overall I don't think any kind of white or cream is going to be your best look. The two lighter-background pieces are going to get lost. What about using the lighter green of the floral print?

Ahh, now I see your colors. Do you have sheets of paper you can place under a section to get a feel for the look?

Warm.

warm will age better than a cool white, and is more pleasing on the eye.

Cool white won't work with the golds and beige. You could do a warm white that is similar to the background in the lightest small pattern block, or you could use another color. I would take the swatches along to a fabric store and see what you like together.

Does she have another print or solid to replace the tan blocks? They dominate the pattern so far. Try printing out a bit of the Ruggable Strawberry Thief colorway or put the squares directly on the Ruggable to see what goes well.

Warm white will be nice