it's useful to have your confirmation e-mail, or booking reference written down, but very often I don't have to show anybody anything; I just state my name and destination, and that's usually enough for the check-in agent to find me on the system.
I've never bothered with luggage tickets. But I do take a photo of my bag & carry it with me; tho' I've only had to use a photo once, when KLM left my bag in Amsterdam - I got it back the next day.