Of those I delete the obviously-terrible images, where the exposure was off, the person blinked, or had their mouth open in an awkward position as we were talking during the shooting process.
The result of a good shoot is 20 images that are worth publishing, and a poor shoot might result in only 10.
All my images are RAW (.CR2), so they're pretty large. Despite that keeping them all is the only approach I feel comfortable with.
Backups are handled by archiving to a local NAS, and uploading offsite once per evening. I'm careful to ensure that when I import the images to my desktop system I don't erase the CF cards before I have that offsite copy uploaded (which sometimes takes a few days).
