He defeating Kizaru in Alabasta, a character we know is quite strong, would be good way to establish he as a strong enemy for Luffy, because now that Luffy will defeat Kaido, BB dont seems like a big threat strongwise.
I believe BB is after Pluton that is in Alabasta, the WG want to take control of Pluton for the cleanesing, but BB will take it for him.
After taking Pluton his bounty will go to 5b and he will be seeing as the closest to become the PK, with 4b Shanks and 3b Luffy after. And making for a good fight where Luffy will still be the underdog like always.
Belive his fight with the SH will happen in the end of the NW, and thats when Franky knowlodge of the weapon will come in hand, and he moving Pluton to the NW will be how the SH will use Pluton power to destroy the Reverse Mountain. Could even be that for the full power of Pluton to be used the head of the Nefertari family is needed, thats why the WG killed Cobra and tryied to kidnap Vivi, and thats how Vivi plot will connect with the crew again and she will rejoin for Laftel and the War against the WG.
And of course there's the Light vs Dark theme, the new admirals having plot armor and being a serious samurai and a woman lover, making for Akainu, Fuji and Ryu being the perfect trio to fight Luffy, Zoro and Sanji, while Kizaru is kind the random admiral.
The only thing that make me confuse is Aokiji, could be that he help BB kill Kizaru to show he can be trusted by him, but we know he isnt a bad guy, and probably plan to give his life to kill BB when the opportunity arrive, i just dont belive BB will kill him now because his plotline hasnt been developed, while Kizaru dont even have a plotline.
There's even theories that BB will take Pluton from Alabasta and blow the Reverse mountain from the Paradise with it, to try to get to Laftel from the other side.