Without Griffin (and Paul in my case), we'd wish their series and Bulls' be done with as soon as possible. It's unlikely, but sweeps on these series will mean we don't have to labor much on picking aside from DeAndre Jordan and the Bulls' Three:
Gasol is the clear choice, especially that he doesn't have to work hard on defense with Kevin Love inactive. I just think Love will not return anytime during this series, that we can wait to pick Gasol at home.
Butler is having a career year and is highly dependable. His counterpart J.R. Smith is suspended for Games 1 & 2, but I think that benefits the Cavs more because now the defensive-minded Iman Shumpert will be guarding Butler. We can wait to pick him later for when he faces Smith who is a one-dimensional player.
Rose has the lowest PRA of the three but can explode in any game. He is also highly prone to injury. Noone wants anybody to get hurt, but I am picking him now for insurance's sake.
If you still have Griffin, and Paul remains hobbled by injury, pick him now because he will have to shoulder much of the scoring. Expect more of those back-to-the basket plays.
Good luck with your picks!