Rey is definitely NOT Luke's daughter, NOR is she Han and Leia's daughter. Who her parents were doesn't matter, aside from the fact that at least one of them was part of the original Rebellion and fought with Han, Luke, and Leia (you can tell because she has a Rebel pilot helmet and a Rebel pilot doll in her home).
Rey was one of the other Force-sensitives who Luke took to train as the next generation of Jedi. This would explain A LOT of things from the film.
It would explain why she had the flashback—to her as a little kid, being taken away from her family and crying, and the separate flashback to Kylo Ren and the Knights of Ren slaughtering all of Luke's other pupils—when she first comes into contact with Anakin/Luke's lightsaber. It would explain why she knows how to command the Force (at least to some extent), and why she clearly has a better idea of how to wield/duel with a lightsaber than Finn—who was top of his class in literally everything, especially hand-to-hand combat—does.
Obviously she received little training with the Force, which is why she had been forgetting to use it while dueling Kylo near the end of the film, until he mentioned the Force. It would also explain why the Resistance was willing to have her go by herself to find Luke. Lastly, it would explain two more things, both from the final scene. It would explain why Rey is on the verge of tears when she finds Luke, and why Luke has a look of sheer surprise and/or amazement that Rey is the one who found him (you can see it in his eyes).
Perhaps the look on Luke's face is actually surprize and/or amazement that Rey is alive. Maybe she barely survived the slaughter of Luke's pupils, but suffered amnesia, which is why she only remembers bits and pieces of any events before that.
I do know the old man in the opening scene of the film—who gives Poe the piece of the map to find Luke—was one of the Rebel soldiers who served under Leia in the original Rebellion, because he says that to him, she will always be royalty. This is also evident in the fact that he knows who Kylo Ren really is, and tells Kylo to "remember [his] family" or to "remember where [he] cones from" (I don't remember exactly how it was worded), before Kylo kills him. It's possible that that old man was Rey's father.
"I can sense you're fear. You're scared that you'll never be as powerful asDarth Vader."
~Rey to Kylo Ren