So I really like TFA, but I’m not a fan of all of the coincidences, such as the missing piece of the map being in the same county as the Falcon, which is in the same county as Rey, and all of them going to a place with Luke’s old lightsaber, etc. I’ve been thinking about it, and here’s how I would handle them if I was in charge of the backstory:
Luke is training a new crop of Jedi, and Ben is an unstable student of 17. Luke gives him his old lightsaber with which to train. However, the lightsaber causes visions of Vader, it’s first master, to appear in Ben’s head. He goes mad and kills everyone, except the 7 year old student named Rey, since he’s still fighting with the light side of the Force. He puts Rey on the Falcon, which was a gift from his dad, and abandons them on some godforsaken world. They are then found by scavengers, bought and sold multiple times like so much property, until winding up in the hands of Unkar Plutt. Ben becomes Ren and leaves for the First Order.
Luke, meanwhile, is disconsolate. Having failed utterly in his quest to train Jedi, he leaves his old lightsaber, tainted with the atrocities of the past, with Maz (who is the most trusted associate of both Luke and Han) and goes off to search for the first Jedi temple. He knows that R2 has a very rare full map of the galaxy in his files, so finding this temple is possible for him. Finding the temple, he leaves a portion of the map to the temple in the hands of his old friend and fellow Jedi teacher Lor San Tekka, deleting that portion from R2’s memory and putting him in low power mode before giving him to Leia. He has had a vision of his daughter on a desert world and feels that his daughter is still alive, so he tells Tekka to go and search for her and watch over her. Finally Tekka finds her and the Falcon on Jakku, and stays there.
The portion of the map given to Tekka has a beacon on it, which will activate R2 if brought in close proximity to him. This is a safeguard, ensuring that the map does not fall into the wrong hands, but also allowing Luke to be found if the galaxy needed him again.
In this backstory, it doesn’t really matter if Rey is Luke’s daughter or not. I just find it too coincidental that she just happens to be strong in the Force, so she must have had at least some training.