It's hard to guess, but here's my bet (in order):
- Gaban vs. Sommers (Gaban wins);
- Roger vs. Kaido (Roger wins);
- Linlin vs. Saturn (Saturn wins, but Linlin gets Kaido's DF and later gives it to him);
- Gaban vs. Kyo (Gaban wins);
- Rayleigh vs. Shiki (Rayleigh wins);
- Newgate vs. Garling (Garling wins);

I agree with Gaban v Sommers...although I don't actually think we'll see or even hear about it. I feel like most of God Valley's fights will be off-screened, with some major peeps not even being mentioned to have been in a particular fight.
I don't think Garling should be able to beat Newgate, especially since he has his fruit, and if Gling has clashed with Rayleigh prior. I don't think he'll beat Newgate, just scar him.
I don't think Roger will beat Kaido, but it would be neat to see.
Linlin should be able to kick Saturn's ass even with his regeneration, and I don’t think they'd fight just for Linlin to lose because she can't finish him off.
I get the whole axe thing, but I don't like the idea of Gaban getting two fights that he wins, but it could happen. I'd be interested in seeing Shiki vs Kyo, since they ARE rivals.
It's entirely possible that Kyo is a marine spy and that there were two traitors in the Rocks Pirates (with or without being connected to each other). Regardless, the two could get into a fight anyways, just because of the animosity they already have for each other.
I would be PISSED if Rayleigh beat Shiki. He should ABSOLUTELY be weaker, but I wouldn't put it past Oda to do something like this anyways.
It would never happen, but I've always wanted a God Valley teamup between Rayleigh and Bogard (both swordsmen, a parallel to Roger and Garp teaming up). I would be more accepting of them fighting against Shiki together.
I don’t think Garling is gonna lose to anyone here.