We recommend keeping background images light, so they load as fast as possible on any browser and device. 
Since background images are only visible on screens on the preview on your store (we never use them for printing) you can keep them light easily without compromising quality.

The recommended dimensions for background images are:

This is a suggestion, any value around that will work well.

Keep in mind that preview images don't need to be square, but it's usually what works better with stores' layouts and product galleries.