Firstly: as of two weeks ago I'd never seen this show, I've now caught up to the current episode: Oh My God why have I not watched this already!?
Secondly: It's called a Song of Fire and Ice in the books, right? (Or at least one of them is) So I reckon it's got to end up as Dany Vs the White Walkers. The Stark kids who are currently training will have to come back to the fore eventually. I can see Jon Snow joining up with Bran and taking the Willings south to Winterfell, possibly with Theonne/Reek turning up for revenge then having it out about betraying the Starks and redeeming himself/dying horribly.
I like the theory about Tyrian Lannister having Targaryen blood somehow, perhaps through an affair by his Mum. I think Dany will have to leave where she is now because of the uprising and will be forced to move on Kings Landing. Tommen will die in the siege and Cercei will escape with Jamie and the big fucker. Then I reckon it's more likely that Snow and Dany will team up against the White Walkers due to Dany's soft spot for underdogs and the Wildlings.
But honestly, I could be completely wrong, I love how unpredictable this show is.