If Bran's vision is true then Bran is heir to House Stark, followed by Sansa then Arya. Jon is only fourth in line even if legitimised. However, if legitimised he does become heir to House Targaryen. He could marry his aunt to cement the claim, although she can't have children so it would mean the end of the House. Better if it does all come out that she names him her heir.
And of course if it comes out he won't be King in the North for long. Bran says he doesn't want to rule, so Sansa is next in line. I'm certain she's going to spill the beans in a really horrible way the moment she finds out. Arya and Jon were very close growing up, so to do this she's also going to have to remove Arya from the game, or at least try to.
I can see Sansa joining The List.
I don't know about Sansa being added to The List, blood being thicker than ink, but I do have the feeling Sansa will not meet a happy end. Something about too many lessons learned from Cersei, the close ties to Littlefinger, etc. We have the contrast of both Dany and Jon motivated by the good of the people, while Sansa seems more of a traditional feudal ruler, someone who might age into an Olenna Tyrell, given the chance. Whatever Sansa's fatal flaw, I don't think it'll be a conscious betrayal of House Stark or her siblings - the Starks, of all noble families, have been "raised right." While the series is in need of the occasional shocking betrayal, I think the Stark's reputation needs to survive intact.
I also don't see Bran spilling the beans until the series' end, a revelation that cements the legitimacy of the new realm, solving the problem of succession. It's not likely the Three-Eyed Raven would confide in either Sansa or Littlefinger.
Not that predictions matter much, but I figure Bran moves back north of the Wall when the series has its happy ending, to continue the Raven's work. Sansa, as already hypothesized, will be out of the picture entirely. Arya completes her List, saving the Worst for last and perhaps rescuing the population of King's Landing from a fiery end in the process, but she falls in the act - she's not made for a world at peace. That leaves Jon, who is more beloved in the North than any other living Stark, Resurrected by the Lord of Light, Heir to House Targaryen, Cousin of Dragons...
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