I, personally, think the most important things to know as a beginner are the parts of the intrument, how it works, and how to properly hold and play it. With this foundation, I feel that it's easier to comprehend what you're supposed to be doing. Creating "bad" playing habits may make things more difficult in the long run.
Tuning. I am very picky when it comes to tuning. I believe that every musician should know how to properly tune their instrument by ear. I can not stand hearing someone play even slightly out of tune. To me, it makes your skill level look...less than perfect, to be nice. Knowing when you're out of tune is a great, simple skill. Knowing how to quickly get in tune quickly is priceless to me.
After that, how to read and play basic chords and have smooth chord transitions (for stringed instruments). Since I can't read music 100%, I would then move on to reading tabulature.
I have taught a handful of people guitar, and have had great results. Most importantly, have fun with it.