He'll likely start off by hanging back and not feuding with any one particular person for about the first month or so. He and his "family" will just observe the other wrestlers while they (or just Wyatt) defeat nobodies in the ring whose only purpose will be jobbing. I'm thinking of how Undertaker was running the Ministry Of Darkness in late '98/early '99 and how aside from feuding with Vince and his Corporation, he was sort of not in direct conflict with any one particular wrestler, rather he was just watching from the back and trying to pick which guys he wanted to "convert" into his Ministry and whatnot. Like Mable in early 1999, for example.
Eventually, after a short while, Wyatt will come upon someone who he thinks would be a good fit for his family and then a rivalry will start brewing when said person wants nothing to do with them.