The big question on the minds of every Game of Thrones fan watching season seven is who will eventually sit victorious on the Iron Throne? Basically there are four houses in the running for this and I'm going to take a look at their prospects of winning.
PROS-If Jon Snow leads the north and anyone else who fights to victory over the White Walkers then his stock will be pretty high among nobles and poor alike. He has the bloodline of Stark and Targaryen, which could unite people in the north and south, especially former supporters of The Mad King. Jon ended the war between the wildlings and the Night's Watch and will have them fight with northmen to defend the Seven Kingdoms. Varys might well come to see him as a better option and if Dany turns mad, Tyrion could desert her too with Jon as a viable option.
CONS-Jon doesn't want to be King in the North never mind sit on the Iron Throne. I feel he would be happy to live at Winterfell with Ghost and Arya! Never mind Sansa, she sucks! He is still thought of as a bastard son of convicted traitor Ned Stark in King's Landing so until his real roots are declared, he would have no chance. As a Targaryen son, he would be in direct conflict with Dany if he wanted the throne and does not have an army to match the Dothraki or dragons if things turn hostile between them. He is untested as a ruler in the type of political environment that Lannisters thrive in and I can't see Ghost at King's Landing.
PROS-Dany has a large army of Dothraki, Unsullied and dragons to make most people bend the knee to her. She is a proven leader of people and the day to day running of things as seen in Meereen. The Targaryen name may still command some respect in Westeros and she really does want to change Westeros for the better so the people could grow to love her as the former slaves have. If she can show the people that she is changing things for the better for them, they would probably follow her.
CONS-The people of Westeros are more likely to fear her than love her, comparing her to her father who burned people with wildfire. Nobody will welcome Dothraki hoardes and Unsullied into King's Landing and will see her as the foreign invader that Cersei had labelled her. Her desire to burn her enemies will always be an issue and if another option came along, the people might turn on her.
PROS-Gendry is the son of Robert Baratheon and though he is a bastard he is Robert's son which Joffrey never was. The current Queen murdered House Tyrell, sleeps with her brother and may wed a Greyjoy so the people wouldn't bother much about a bastard ruling if he was a good King. The poorer people in Flea Bottom might have high hopes for a ruler of their own as that is where Gendry was born, and he would want to see things get better for them. Perhaps he could get the backing of those who were loyal to any of the Baratheon brothers, especially if they see him on a horse with his hammer like Robert in his prime. He would be a good bet to marry into power-Sansa, Dany, Arya.
CONS-Gendry wouldn't want to rule the country. He has no leadership skills, battle experience or sense of politics and how to rule. He would need excellent advisors around him but would the rich be loyal to him after deposing Cersei? He has no rich or powerful allies so he would be a very long shot.
PROS-Cersei currently resides on the Iron Throne behind the protection of the King's Landing walls. I expect that her pyromaster has been hard at work making more wildfire in case Dany's ships come to the bay, having learned from Tyrion's tricks. She has The Mountain as her personal bodyguard so it will be tough for anyone to kill or capture her. She has ruthlessly dealt with her enemies and has a sharp mind and intinct for how to play the game and win. Qyburn is also a master of tricks with a good spy network and Cersei has survived one battle for King's Landing, defeating Stannis. She has the naval backing of Euron Greyjoy.
CONS-Cersei is not well liked in Westeros and if Dany convinces the people and soldiers that her way is better, they may fight for her. She has already lost a portion of her army to Dany and lost the supplies they took from Highgarden so a long siege could be a problem. Tyrion knows King's Landing and it's strengths and weaknesses even better than she does. If it looks like they are losing the war, very few would stay loyal to her.
PROS-Tyrion is the other option. He is intelligent, politically minded and knows how to play the game. He is not cruel and he did save King's Landing from Stannis. Varys would be invaluable to him. If something happens to Dany, he would be able to control the dragons but would be less likely to use them the way Dany does. There is still a possibility that he is of Targaryen blood which would make him Dany's older brother and a better claim than she has.
CONS-He may have problems with loyalty as he is still accused of killing Joffrey and did murder Tywin. Would men trust a man who killed his family? As a dwarf he does not have the respect of people and lacks the ruthless nature of his sister. If he is actually Targaryen his claim is better than Dany's but Jon's is better than both of them. He is more cautious and less ruthless so would he make a better leader or a less effective one? His decisions are not always the best.