Have her still be a junker and salvager on the planet, and have her still being someone of simple means, but have her have some agency. She's not just salvaging trash to sell, she's self-taught and has a goal in mind. Have her have salvaged an old Y-Wing or something with an Astromech socket, and have her be trying to get the fuck off the planet she's on, but the ship isn't finished enough for high altitude flight yet and even if it was, she wouldn't be able to leave because ships this old don't have nav computers so she can't use the Hyperdrive. She'd also need an astromech.
When BB8 first appears, have Rey initially interested in him specifically because he's an astromech, not because of anything greater. The little guy is literally a ticket off that world if she can fix the rest of the ship. Have the trader offer her a quite literal king's ransom in return for BB8, something that she'd get legitimately tempted by. Does she abandon the dream for the sake of living in the lap of luxury for the rest of her days? Why the hell does the trader want the little bugger so much? It sets up a good momentary conflict and helps establish her flaws, and her strengths, since she'd ultimately side with BB8.
When Finn arrives, have it be less of a chase off planet and more of a race against time. Finn needs to get back to friendly territory ASAP with the First Order hot on his heels, and needs to stay off the radar while doing it. Rey overhears and hey, she's got a ship almost ready, so she offers to take him to the planet in question if he helps her with the final batch of repairs. This can even lead to some humorous overtones to the OT, if slightly subverted. Rey gets the ship ready, maybe talks about being abandoned, gets excited when she hears Finn's with the resistance even if he's lying, it can even set up some interesting interplay with BB8 and Finn.
When she meets up with Han, have the circumstances be very different; the two meeting, more-or-less, by accident when refueling (and repairing) her Y-Wing for the 99th time. Han realizes she reminds him of Luke in quite a few ways, and talks to her about him. Having a bit of a nerd-out, Rey asks about what happened, how the First Order rose to power, and why Han's in the middle of buttfucked nowhere. All this helps lead to better character and world building, and sets it up so that if you really must kill Han off in the movie, it has a much bigger impact on Rey.
Characterization-wise, I'd have Ray a bit more naive, but also way more hard-edged. She's initially distrustful of people but also kind of idealistic. She's been abandoned by her parents so she's somewhat weird around people she doesn't know well, and tends to focus more on the immediate than on the long term, not always to her benefit. With those she actually cares about, she's incredibly trusting, which can make for some interesting developments. She wants to do good but she's not above some minor selfishness as I posited in BB8's example, though she eventually does legitimately befriend him.
She's really good with tech and frequently can come up with unorthodox solutions to problems; her ship is a Frankenstein's monster of engineering under the hood, with parts from almost a dozen Imperial vessels that were never intended to be shoved in the frame of an old Alliance Y-Wing, but which have been and the results work, though they're as finicky as they are powerful and Rey often has to crawl around on top of the thing to get it working between flights. Have her show some force sensitivity, but not really know anything about the force beyond that it existed.
The way I did it accomplishes a few things: It allows for growth, it establishes her as having skills, it parallels her to the original characters without huge amounts of overlap, we get a grasp of her strengths and flaws, we use her to get a grasp of what the situation is in the universe right now, and we get our first taste of the adventure to come. All good things, and I really didn't need to do a fuck of a lot to make it happen.
