After seeing the Last Jedi a few times, I have some ideas. Safe to say, spoilers ahead, you have been warned!
Next big bad: General Hux
Why? He didn't hesitate to draw his weapon when Ren was unconscious on the floor. He didn't have the time to kill Kylo Ren, as he just came to.
Also, you could see he barely believed the story that Rey was able to kill Snoke, the entire pretorian guard and knock Ren out.
The First Order doesn't work the way the Sith did. There it was expected for the apprentice to kill the master at a certain point and take control, no questions asked.
It doesn't work that way with the first order, cause when you look closely you can see they are Hux's army, before they are Ren's.
Hux will find out Ren had to do with Snoke's death and Ren will be removed in some way.
Identity crisis: Kylo Ren
Rey has learned that the good guys also make mistakes, the way Luke did and that the Jedi order, as is, needs to die. She did take the Jedi scriptures and hopefully she will glean some insights, supporting what Luke said. Through her Force bond with Kylo Ren, she also learned that evil stems from hurt, abandonment and betrayal, much like she has experienced. Thusly opening the path, in my opinion, for a more balanced approach to the Force.
The Force and Force bond.
It's obvious something needs to change, the Force is all about balance. There is good in the world, and there is bad. Life, death, etc. The word balance gets thrown around a lot and I believe that is were we are headed. Both the Jedi and the Sith are entirely too absolute. No attachments, no (romantic) love, no strong emotions as opposed to fully utilizing your impulses and passion to achieve your goals.
The Force bond between Ben and Rey is obviously not gone, as we see at the end of TLJ. Some believe this is Rey's final act of literally, closing the door on their relationship. I don't think it is. It's very obvious since the beginning that these two have a different vibe about them.
In the Force Awakens, Rey gets 'preferential' treatment as a prisoner. Poe gets beaten, dragged, beaten again and then interrogated by Kylo Ren. Not so with Rey, he carries her, she doesn't get 'softened up' and he actually stops 'probing' her mind once she says to get out of her mind. He also the only person who never lies to her. When she asks about her friends, he tells her honestly he doesn't know. Nor does he ever lie about Luke, her parents, his intentions, etc. I mean, even Finn lied to her in the beginning, understandably so, but he still did.
So yes, all that build-up to have it end that way? I don't think so. The connection is still alive, even after Snoke's death, so they find out. Even if he did bridge their minds in the beginning, I think only they are responsible for deepening and maintaining the bond. I even think Snoke had little to do with the bond. He sensed it through his apprentice and used it as yet another insult, another way to keep Kylo Ren small and humiliated.
So yes, there will be much soul searching and pain to live through before these two can begin to heal their wounds. But they will, and they will join up, and both will turn, but not to the dark or light, but to a balanced path that takes everyone into account.
The Resistance, supplemented by Rebels all over the galaxy, by First Order defectors and Ben Solo against Hux' First Order that will end up in a New Order, no ties to the Old/New Republic or the Empire, just something else.
Edit: Plus Rey makes a double bladed, staff like lightsaber. Yellow. I think.