First off, Chloe continues to be completely worthless. I sense this will be a running theme. Also, Eli needs to grow a pair.
My favorite bit of the episode was Riley and some of the others giving Eli the pat goodbye during the selection. It's a very subtle thing, but it was a nice touch. Also in that scene, some of the soldiers are harassing Eli for information in the beginning... another small touch that I enjoyed. Also, Eli figuring out what Rush was suggesting with the slingshot, and immediately working on the calculations before Young caught on. They do a lot of subtle stuff with Eli that way.
It was obvious that Johansen was going to be one of the two chosen ones from the beginning. A medic is the absolute essential need. Once Scott laid out how he was the only qualified pilot, most of the suspense there was gone.
I too fully expected them to use the Stargate, especially since they made sure to get the countdown clock in several of the background shots. The shuttle looked to be about the same size as a puddle jumper (plus the Ancients made both) so I figured they'd fly it through. Ah well.
A bit of continuity problem - if the shields were blocking the radiation on heat, why were their faces red? Oops.
I don't think Rush knew the shields would hold. However, I also think he suspected the ship targeted the sun for a reason. For Rush, I think it was a matter of faith, and most of his scenes in this episode reflect that. He threw the book because his faith in the Destiny, and even in science if you want to extend the metaphor, waned.
Of course, the final scene demands some kind of analysis. First off, the scene was deliberate callback to the pilot, when Rush wasn't even invited to the table, and Eli was.
I think that while there is some resentment about the leadership, I don't think that's the big thing between Young and Rush. I think that the two fundamentally don't understand each other, and that's the cause of the tension.
First, as Fast Learner said, Young was being fairly condescending towards Rush, from Rush's point of view. However, if you take it from the point of view of Young, that's how he, and many of the military people we've seen here and on other Stargates, show appreciation. The soldiers are physical people; they'll celebrate by high-fiving and head-patting and all sorts of touching. That's just how they are. Even outside of celebration, it's the soldier that puts his arm around Wray to comfort her. Contrast that with the scientists, who are generally distanced from physical contact - they're in the realm of the mind, and you celebrate in the same way. It's Chloe that takes Eli's hand for comfort, not the other way around. Sure, Eli will sit at the table with the soldiers... but he wasn't nearly so animated as the others.
Second, I think Young completely misread why Rush took himself out of the lottery. Rush may have kept to his faith that the ship was going into the star for a reason, but I don't think that was the only reason. Faced with the idea that it was his obsession that would kill everyone, I think there was a large amount of guilt involved as well. It's all well and good if he gets himself killed in pursuit of his beliefs, but not everyone else.
Finally, the double rations thing was simply a way of Young saying he was sorry, and trying to be conciliatory. This again goes to the dichotomy between soliders/physical and scientists/mental. That is, Young wanted to give something material to Rush to make amends. Rush wanted something ephemeral - he wanted respect and trust, and didn't care about extra rations. Bringing it around, Rush shows Eli respect and appreciation not by giving him anything, but trusting that Eli was right.
So it's not really a Rush thing, or a Young thing - it's a differences thing. That's what moves it beyond being tension, and actually moves it towards the realm of tragedy.
[EDIT]One other thing that bothers me. It's been a while since I've seen SG:A, and I don't have much desire to watch it again. Didn't Atlantis have databases with the knowledge of the Ancients in it? I would presume that would include some way to power the ninth chevron. For that matter, I would assume Destiny would have a way of powering it so the Ancients could travel back from the ship. Maybe this is something that will come up, or would have been part of SG:A had it gone on.