The order I formulated was 1-4-2-5-3-6 (then 7 when it comes out, assuming it doesn't tank). This is by far the best way to show someone the movies without spoiling the big reveals. I'll briefly touch base on why this order makes sense *POTENTIAL SPOILERS*
Episode 1, if you may not recall (for any number of reasons) introduced us to Obi-Wan, Qui-Gon, Yoda, Anakin Skywalker, Senator Palpatine and Padmé Amidala. (Skipping the droids because they're both in all six movies, so yeah) While it's more than obvious that Padmé is going to probably end up with Anakin in the near future, for the outside observer you don't get much more than a "meh" from this movie. I think there's a space battle? I'll be kinda honest, it's the weakest link out of the six (seven), but it's best to get it out of the way now to let the other 5 (6) build up more.
Episode 4 is the true introduction to Star Wars for most of us, and it introduces Luke Skywalker, Han Solo, Chewbacca, Princess Leia, and reintroduces Obi-Wan as a wizened Jedi Master, who sees Luke and remembers the boy that Luke's father was (wooOOOooooo plot connection!). Luke and cast leave Tatooine, with Luke swearing he'll never return. We are also introduced to Darth Vader, an evil Jedi who we are told killed Anakin. This is probably never mentioned again whatsoever in any other movie and probably isn't special trivia at all.
Episode 2 now introduces the beginning of the Clone Wars, mentioned in passing during Episode 4 when Obi-Wan met Luke, and it also introduces us to Jango Fett and by proxy Boba Fett. We also get to see how awesome Jango is fighting a Jedi. We also see a fight scene with Master Yoda and Count Dooku, which leads us into Episode 5. Jar Jar Binks basically puts Palpatine in charge single-handedly after being manipulated, way to go Jar Jar. Reason #4,312 nobody likes you. Oh, and we also get to meet the first generation Stormtroopers. Way to make 'em worse later, Empire. Also, hints of Anakin's rebellious nature, including his attraction Padmé that was basically shouted at us since the first movie.
Episode 5 is the big reveal movie, basically. Luke meets Yoda, Vader's not dead, we meet Lando Calrissian, Han is betrayed by Lando, Luke is trained, Luke enters a cave, Luke senses trouble after the trippy cave scene, he goes to Cloud City, Han is taken to Tatooine by Boba Fett (remember him from up there ^?), the big reveal is made, hands are lost, Luke is rescued, and the movie basically ends on an even worse cliffhanger than Smaug attacking Lake-town. (I am... death.)
Episode 3 is where the big reveal leads us to the inevitable demise of Anakin Skywalker and the rise of Darth Vader. Basically, it's the birth of the Empire and so on and so forth. But we do get an epic fight scene between Palpatine and Yoda. Still didn't save the movie for me, IMO. Next movie!
Episode 6 is the movie that takes it all home for us. (Until Episode 7.) Pretty much Empire builds a new Death Star, the Emperor arrives on the new Death Star, The cast returns to Tatooine against Luke's will, they get captured, and Luke single-handedly rescues half the cast from a giant slug. Later, many Bothans die to get information about the Death Star II to the Rebels, we are all sad but can't remember what a Bothan is, then the entire cast except Lando go to the forest moon of Endor (why a moon? Why not the planet Endor? Whatever.) to disable the shields on the clearly disabled Death Star. Turns out, it's a trap! and they're ambushed. Luke fights Vader, Ewoks happen, the Emperor is defeated, Vader dies, Anakin is avenged, and finally Force ghost cameos for all.
... I'll admit, didn't quite expect to write all that, but I said whatever, nobody reads my blog anyway
To summarize (TL:DR), 1-4-2-5-3-6(-7) is probably the best way to introduce someone to Star Wars, assuming they haven't seen it before or were spoiled in any way, shape or form. I'm sure people will disagree, but I hope my rather long arguments for this reason will sway you to see it my way.
Besides, you could always keep ignoring 1-2-3 if that's what you'd prefer. I won't judge you, I'm only socially obligated to even have those DVDs (Actually, I didn't mind 1-2-3 as much, but I could go on even longer rants on how I'd fix those personally. This is why I don't rant much.)