Reply To: Fixed background image scrolls on phone

For the best image size, I would say it is a matter of personal preference, but I would say you could look at using an image with a narrower width in relation to the height for smaller devices such as phones.

Then use a media query in custom CSS to use the alternative image on mobile only, like so:

@media (max-width: 768px) {
    body.custom-background {
        background-image: url('my-image-url-alt-phone');
    }
}