I think there's a distinct possibility that all three play, as well, though for perhaps different reasons.
I think the depth chart will either have all three QBs listed as starters (1a, 1b, & 1c) or will have Bateman and Barnett as co-starters and Hurts as the backup. Regardless, I think the outcome will be the same. I think Bateman comes out to take the first snap - assuming the first snap isn't a wildcat thing or something like that - and probably takes the majority of the snaps in the first half.
I also think Hurts will definitely play some in the first half but I don't necessarily think it'll be a like-for-like swap with Bateman. I think Hurts will have a "package" of plays designed to optimize his talents but also reduce the amount of decision-making responsibility being placed on a true freshman. He'll be used more as a change-of-pace to keep the defense off-balance, giving them a different wrinkle to have to think about.
If the game stays close and Bateman is playing well enough, Barnett may not see the field in this one. However, if we get a little bit of a comfortable lead or Bateman stinks it up a bit then Blake will definitely get some snaps.
Going forward, I think we'll start out running a faux, two quarterback system with Bateman/Barnett seemingly vying for the starting job with Hurts primarily running the change-up package. I do think, though, that Hurts will be given some chances against Western Kentucky and Kent State to run the whole offense. I think Bateman is in the driver's seat for earning the starting job but Barnett could take it from him if the light flips on and he turns out to be a gamer, where his inconsistency and tendency to force the ball into coverage disappears. Of course, if neither of those guys proves able to adequately, consistently guide the offense and Hurts plays well with all he's given, I could see Hurts being named the starter by either the Kentucky or Arkansas games.