Mine would be probably similar to the existing one in broad strokes. One of the changes I’d definitely do is turn the Resistance into the New Republic to avoid extremely overt OT parallels, and play with the political rivalry that exists between Leia’s militaristic faction and those who don’t believe in the threat of the First Order. They would lose their capital at Hosnian Prime at some point during the second film, this way setting up the “loss of hope” sentiment.
Another important change is that I would spread the events across a time span of five years rather than one (and no films starting right at the aftermath of the previous one). This way character progression is more understandable and less people would have issues with Rey’s power levels.
In my version the First and Final Orders would be merged. I’m split on having Palpatine return in the flesh (maybe I’d have his return revealed as a cliffhanger ending for the first film), though the First Order would be a direct result of his contingency plan after the Battle of Endor, and be very dark side-inspired and be something of a theocracy. At the centre of this hierarchy would be the Knights of Ren, with Snoke or a stand-in for him as the master of their order. Kylo becomes the master of the Knights once he defeats Snoke midway through the second film.
Rey would not be a biological Skywalker, Palpatine, etc. Her power is random like any other Jedi’s, but enhanced through the story because of the Force dyad, that would also be established much earlier.
Finn becoming a Jedi and leading a stormtrooper revolution would be definitely a part of this alternate story.
The galactic underworld would also have a big play to part.