Whatever your reason, if you are showing someone the official editions of Star Wars for the first time (no Phantom Edits), you have to make a decision about which order to show the films.
Now I'd like to modify this into what I've named Machete Order on the off chance that this catches on because I'm a vain asshole.
Next time you want to introduce someone to Star Wars for the first time, watch the films with them in this order: IV, V, II, III, VI
Notice something? Yeah, Episode I is gone.
I recently discovered my college-aged brother-in-law's girlfriend had never seen any Star Wars films and wanted to watch them all over winter break. Armed with the new Blu-rays, we all went about watching them, and I showed them in Machete Order. It actually works even better than I originally anticipated—it's almost as if this is somehow the intented order. There's a great pattern here, taking the viewer on a series of emotional ups and downs. IV ends with a victory that seems to have some sinister undertones, then V is dark and unresolved with a cliffhanger, II ends with victory with sinister undertones, then III is dark and unresolved with a cliffhanger again. It works incredibly well, and when III ended everyone demanded we immediately watch VI to see how everything gets tied up.
I asked her if she found Jar-Jar annoying and she asked “who’s Jar Jar?”—Mission accomplished.
There's not much to say about this other than “you must read this” (that is, if you at all a fan of Star Wars). The new ordering of viewing makes “Return of the Jedi” a much better film than it deserves to be (it's the weakest of the original trilogy) and resolves both Luke's and Anakin's storylines from the previous four films.