Spoiler Warning, if anyone still hasn't seen The Force Awakens.
This is not a discussion of if Rey is biologically a Skywalker or not, maybe she's Luke's daughter, I think her being Han and Leia's daughter is still more likely then that. I also like the idea of her being Palpatine's clone. But this post isn't about her ancestry, it's about her narrative role in how this Trilogy echoes the first two trilogies.
I fully agree with those who say it's inherently Sexist to call Rey a Mary Sue to demean her, like BrosWatchPLLToo and TheMarySue. However there is a good reason for critics to feel vindicated in saying her victory here goes beyond Luke's awesomeness in A New Hope.
In the previous Trilogies, the Skywalker does not win their first Lightsaber battle with a Darkside Force user. Also they don't even get to have said battle till the final act of the second film. Anakin lost to Dooku and Luke lost to Vader, then in the Third film they get to be victorious over the Sith who dismembered them, and made different choices about what to do with that victory.
There is however precedent in the Star Wars saga for a young not yet Knighted Jedi defeating a Darkside Force User in battle in the first film of their Trilogy. Obi-Wan Kenobi in Episode I The Phantom Menace. And his victory over Maul is faaaar more implausible then Rey's over Kylo Ren. Yes Obi-Wan had more training, but Darth Maul was also a far better swordsman then Kylo Ren, and wasn't wounded, and defeated Obi-Wan's mentor without breaking a sweat, and he had the high ground.
Now PT haters do criticize Obi-Wan's victory playing out that way. (I like it, I want Star Wars to be ridiculous and implausible). But they never called Obi-Wan a Mary Sue, they simply complained that the plot demanded he win and so he won. Likewise the story Abrams was telling demanded Rey win, and so she won.
There were even specific references to the Obi-Wan vs Darth Maul Battle. When Rey closes her eyes to focus before turning the tables, that's a very direct reference (so all this TFA ignored the Prequels BS needs to stop).
This reminds me of how in a lot of ways Obi-Wan played the Han Solo role in the PT. Even having a similar sense of Humor in Episodes II and III.
And going to this connection about being the one to defeat a Sith in the first film of their Trilogy, Han did defeat Vader in A New Hope, not a Lightsaber battle but still, Han Solo defeated Darth Vader at the Battle of Yavin, and that victory too is implausible, his ability to sneak up on Vader with no one detecting him given all the tech the Deathstar had and Vader being basically Psychic is absurd beyond belief.
This is cemented by Han Solo playing the Ben Kenobi role in The Force Awakens.
So given that Rey has inherited the Millennium Falcon. I would say it is really Han's torch that was passed to Rey, not Luke's. The Lightsaber is now returned to Luke who'll need it if we do see him in battle again, people forget he doesn't have the Green Saber anymore, he threw it down on the Second Deathstar and it's not likely he picked it back up off screen. I think Rey is going to build herself a Double Bladed Purple Lightsaber.
Now before anyone freaks out that I'm taking away Rey's status as The Messianic Hero of the new Trilogy. I want to go back to my awareness that TFA drew on the PT just as much as the OT. Obi-Wan was The Real Hero of the PT. Anakin become the Villain in episode III and was a kid in Episode I. And even in II Anakin's story was a subplot as far as that film as a stand alone goes, while Obi-Wan was on the trail of the mystery. The PT is like a Batman story where Robin becomes the Villain and Liam Neeson was his Mentor.
Maybe the Skywalker role won't be a Jedi or Force Sensitive at all, just as the one who inherited Obi-Wan's role in Episode IV wasn't a Force User. It's Poe who did what Luke and Anakin did in their Trilogies first installment. Blow up a Battle station piloting a fighter.
In the PT the Sith who would be Anakin's Rival wasn't in the first film. So perhaps one of the other Six Knights of Ren will be a Fighter Pilot who'll develop a rivalry with Poe. And/or perhaps the Skywalker role is being divided between Poe and Finn, since the OT did have two Skywalkers but one of them played the Padme role. And Finn got to be the best non Force Sensitive to use a Lightsaber on the Lightside with Luke's Saber.
So which of them will lose a hand?