If you want to have a nice pic on your desktop instead of the default tinycore one, download it and save it in /opt/backgrounds. Then with the Wallpaper chooser (look in Control Panel), select if from the list.
That's all - if persistence is already up and running for you, the wallpaper will be there next time.
You cannot load an image with a space in it's name, or certain other characters, such as brackets. If an image file has a space, brackets, or other unusual characters, rename it, excluding these.
Bear in mind that images are often very large files, and keeping many image files in /opt/backgrounds will blow out the backup time unnecessarily. Since these are static files, you can also place your image file somewhere else such as in /tce and create a symlink to it in opt/backgrounds.
For a hard drive installation, it is better to use permanent directories for ~HOME and /opt, avoiding backing up.