SPOILERS WITHIN: DON'T READ IF YOU DON'T KNOW ABOUT JON SNOW'S PARENTS
I think it can only be Jon Snow/Danaerys or Night's King. First off, GRRM wrote the books to deconstruct the fairy tale/fantasy genre, but I don't think he'll deviate from the typical ending. Jon Snow and Danaerys are the traditional heroes of said genre. The standard fantasy novel would end with them prevailing.
Of the two, I can't really decide. I'd make a bet on them getting married before deciding which of the two takes the Throne. Jon Snow is a Targaryen so he will either be revived from the fire when they burn his body or as a result of Melisandra's blood magic. Either way, he will be released from his vows.
The winner of the Throne will not be decided by some scheme. This much is clear. The winner will be the party who vanquishes the Nightwalkers. I think John will seize the North from the Boltons and either set up Sansa/Rickon or have his own claim as the son of Lyanna. Bran's alliance with the Children and Daneyrs dragons seem all but set up to be the key to defeating the Night's King. I could see Jon Snow marrying his aunt Daenyrs, and then seizing the throne.
The only other people worth mentioning are Aegon and Baelish. Aegon has not been mentioned in the show and it seems highly doubtful a new character would end up as the winner by birthright, especially with two Targaryens as the series' protagonists. Baelish is positioned to seize the throne before the Jon/Dany scheme, but he won't keep it. He's too smart and wily to deny a Dany/Jon claim if they vanquish the White Walkers. That's the key to the series.
If I had to choose one, I'd take Jon Snow. This would be the traditional narrative- finish what Ned should have done and seize the throne for the Starks + he has the rightful bloodline claim through his father. It'd also be a rags-to-riches story of the falsely labeled bastard of royal descent who rises up and fights for justice.
The Night's King is a nice hedge in case GRRM says fuck everybody and goes through with creating an atypical fantasy. This would be much more likely if I believed he planned on creating a second series with the Night's King dominating Westeros as the heroes regroup in a foreign land.