If I had to pick a king, I think I would go with Tommen. His mother no longer controls him like she once did and he has a good wife who will toughen him up and educate him in the ways of politics.
The boy needs to grow up fast, though. Lots of bad stuff is brewing all around him and most of the people sequestered in King's Landing have very little idea what. Nobody there believes Dany has 3 dragons, or is aware of the other significant goings-on in Essos, nor do they really believe there is any real danger to the north beyond the Wall. They seem completely detached from the Bolton/Stannis/Ironborn struggle up there as well.
Tommen is living in a rather sound-proof bubble and I fear he'll not be there for long.
So, if Jon is really a Targarean and he is the Song of Ice and Fire - is the whole story just going to have been one of the Restoration of House Targarean?
Considering how many there still seem to be bouncing around out there, that may very well be the case, yes. At the very least, play a major role in what's to come. The dragons will need to become a major player in the game. In fact, constant references to the "Game" of thrones and the chess-like game of "Cyvasse" in the story itself makes me feel like all the various "gods" of this world are playing a massive game of Cyvasse, with all the major characters as players.