There isn’t a specific recommended size for background images. You’re free to upload a background image of any dimensions you like to achieve the effect you want. You can also play with settings such as background repeat, fixed positioning, and other options available in the Customizer’s Colors & Background panel, by clicking the Options button: https://cloudup.com/cLDaGVNYCtY
Another thing to keep in mind is that background images will display differently on different sized screens, so it’s best to use an image that can be flexible in that way.
If you’re trying to achieve something specific, just let me know and I’ll be glad to try to help.