This is what I think;
I think Zuko and Iroh will join the gAang. I've read theories that Iroh would stay in Ba Sing Se just because of his tea shop, and I think that's just messed up. I mean, c'mon, we have to give Iroh more credit then that. Sure, he loves his tea, but he wouldn't just go and leave Zuko for something so simple! Besides, I think Iroh is the one who's going to teach Aang fire-bending. Sure, Zuko is a great firebender, but he will never truly advance until he lets go of all his mental comflict inside. I think Iroh would teach Aang and Zuko, but Aang will advance very quickly, leaving a very grumpy prince.
Regarding how well the Zucrew and the gAang get along; Obviously, Aang would get along with Zuko very well, and in my opinion, Katara might start getting along with him too. I think that her confrontation with him in the cave in the season finale will lead to his final descision of him and Iroh joining the gAang. And I don't mean a Zutara romance (being the strict Kataang that I am), just a friendship. I also think Toph may start liking him too. I picture her treating Zuko as the new Sokka; messing with him and all that. xD And speaking of Sokka, I think it will take a long time for our Water Tribe warrior to get along with Zuko. As in, a real long time. I keep picturing Sokka regarding Zuko as a rival, even though they could learn valuable fighting tips from each other. And of course, Iroh would get along with everybody, being the gang's 'Grandfather' figure and all that. Because he's awesome like that. :3