The Jazz will use this draft as an opportunity to get a talent that they can't get from their current roster, through feasible trades or through free agency.
I think they tricked everyone and they'll take Paul George. They need a starting-caliber SG, and Miles is really a SF. Henry is a possibility, but doesn't seem to have the same crunch-time, I-can-create upside.
If they wake up and realize 'Oh sh**, we don't have a center, they might panic and take Aldrich, but I think they would probably pick up a defensive big later in the draft or through free agency. The Jazz have always picked up players like Greg Foster, Adam Keefe, Antoine Carr and turned them into rotation players.
If they are confident they are not going to renew with AK, they might take Babbit, but I don't think he's really a difference maker. I wish he were Paul Pierce, but I doubt it, unless he develops more moves than just a jab-step. He needs to be able to post and slash at his size. Despite his athleticism, he seems a step slow in games. I think he's a slightly better prospect than Aminu though.
If they actually took Whiteside, it would surprise me a bit, but not shock me. I think he adds something the Jazz don't have in a long pick-and-pop PF/C who can play some defense, so he could swing as a back-up to either position and draw a double team in the post. He needs to add strength and learn some moves in the post, but he's no more raw than Ed Davis.
I think Monroe is probably in the top 6 on their board, but it won't be easy to get him. I think the Jazz's board looks like this:
1 Wall
2 Cousins
3 Turner
4 Favors
5 Johnson
6 Monroe
7 George
8 Whiteside/Davis
9 Davis/Whiteside
10 Babbit/Henry
So, there you have it: The top 6 players on the Jazz's board will be gone, and the Jazz will take Paul George.