Gendry if the focus because he's the one in Kings Landing, right under her nose. I also think that Ned's interest in him is a bit more than the love for a best friend's (almost brother in law) kid. I think judging from Gendry's relationship with Arya, they get along like siblings, like Jon and her. I think Gendry and Jon have either the same mother (if it's not been disprove) or their mothers were sisters.
Also, I don't take that whole Bran thing to heart. There are no outright heroes or villains, Septas and Maesters are often superstitious. Fear of the 3 eyed crow, fear of winter, way I see it is Bran is the first to unlock those powers in a long time and he is a Stark so he will probably take the wall since he can't be lord of Winterfell.
