Warning: Spoilers will be cropping up all through this blog post. If you get upset about spoilers when the last book in the series was published in 2011 and the most recent episode was aired a year ago, though, that's your problem, not mine!
I've watched the HBO Game of Thrones series, up to the end of Season 7, and over the past year I've read George RR Martin's Song of Ice and Fire series, just finishing A Dance with Dragons this week. I've seen good, bad and indifferent characters come and go (and those that go most often do so in unpleasant ways). (Almost) All the people of Westeros are having a very unpleasant time, with the prospect of much worse times in the near future. They need some decent leadership, but whose? I am considering not necessarily the best person to wear the crown and sit on the Iron Throne, but who can provide the best leadership. This means that a decent Hand of the King could count as a ruler, either as regent or with a compliant king or queen, and also leaves open the possibility of an independent king in the North, the Iron Islands, or Sunspear, for example.
So let's run through our candidates, shall we?
Robert Baratheon: Disinterested king. Dynamic back in Robert's Rebellion, when he originally claimed the Iron Throne, but uninterested in the petty details of actually ruling. Has delegated power to his Hand and his Small Council. As long as the Hand and the Council are competent, this works well enough but leads to trouble when the balance of power in the council is disrupted. This is of course what happens at the beginning of the series, where Hand of the King Jon Arryn is murdered. So, no, Robert is not fit to rule Westeros, but he was adequate as long as he had good (or good enough) advisors on his small council.
Eddard Stark: (either as Hand of the King, or King in the North) too naive, too worried about honour. Honour is good, and it's important to have honour to direct your behaviour, but as the man says,
Being honourable is excellent, but don't assume anyone else will follow or believe the same code that you do. Amazing that Ned lasted as long as he did even in the North without getting bumped off by someone abusing his naivety, so no surprise that he was among the earliest losers in the Game of Thrones.
Renly Baratheon: Ambitious but not realistic. He knew the dangers that were present in King's Landing, and cleverly got out of there promptly. Charismatic, and quickly raised an army but not sensible enough to treat with his brother first. He knew Stannis well, and knew that Stannis would never step aside for him, but he shouldn't have raised a rebellion against Joffrey until after he was certain that at least his own House Baratheon would be united behind his claim. Talking to Stannis quietly and in private before raising his banners might have allowed the brothers to create a united front. Getting killed by a demonic smoke baby would have been hard to anticipate, though.
Stannis Baratheon: Too rigid. I like that he is a stickler for the 'rules', whatever they may be. His habit of pointing out the distinction between "less" and "fewer" makes me smile. He's a competent commander, and his men appreciate that, whatever his other faults, he will lead them to victory. I was so enamoured of Stephen Dillane's portrayal of Stannis that for a while I was on Team Stannis. Burning his little princess was a stupid thing,though. In addition to horrifying anyone on his side with any decency, it also ended his own bloodline as there was no sign that he and Queen Selyse were going to have any more children. In a land of dynasties, ya gotta have kids.
Joffrey Baratheon: Incapable of ruling on the strength of his own dignitas.
Being a bored, spoiled, angry little boy, he is unsuited to the throne. Had he been taught responsibility and duty, he may have eventually learnt to be an adequate king, but as we know, his career was mercifully cut short. Regardless, it seems unlikely that anyone would have taught him those lessons - grandpa Tywin and unca Tyrion being the only people who had even considered teaching him, but neither seemed to find the challenge worth the effort.
Tywin Lannister: Tywin is a great leader, very focussed, very disciplined. He prioritizes the advancement of his own house but is wise enough to balance out things a bit with awards or rewards for allies to keep them on side. He is not "nice" but in his role he doesn't need to be: he needs to be effective. He is not needlessly cruel, and he understands that there needs to be at least a perception of justice.
In his role as leader of the realm he does very well, however as a father he fails rather badly. He sees his children as his subjects, and doesn't understand when they don't take his orders. He is blind to the incest between Jamie and Cersei, even when Cersei tells him to his face he refuses to accept it. He could have owned it, and with the performance he shown in other matters, he could have even made it into some sort of triumph (considering how much success the incestuous Targaryan kings had). He also refused to see the strengths of Tyrion. Imagine if Tyrion had received even the slightest acknowledgement from his father, the slightest gesture of appreciation. Instead Tyrion gets all the shit jobs, and he turns each role around, saving King's Landing when he was Hand of the King, escaping Catelyn Stark at the Eyrie, recruiting the savage hill tribes to fight for House Lannister and King Joffrey. Tywin should look past the dwarf and see his son. But he didn't, so
Tyrion Lannister: Everyone loves Tyrion. He is so smart, and just rocks as Hand of the King (and latterly Hand of the Queen). I can't see him ruling in his own name, but he is an excellent power behind the throne. He's like a better, more humane version of his father - best power behind the crown, provided the head that wears the crown listens to him (although his advice does get a bit dodgy in season 7...)
Cersei Lannister: She's not a good ruler. Nasty, vindictive, would rather destroy the kingdom(s) rather than rule them well. Not good for peace, stability nor prosperity.
Jon Snow: Very earnest. Very gullible. Strong sense of honour, which is great, and he's learnt not to be blinded by it (more than you can say for his "father", Ned). But he's kind of a dope. He has to trust his closest advisers with his plans. Case in point being when he tells Sansa in front of everybody that she will rule the North in his absence. Not cool - if you want to dump that level of responsibility on someone, make sure you tell them in private, so if they freak out, it won't be in front of the entire population. Sure, getting stabbed to death by one's sworn brothers can really set one back in the trust department, but that you can't rule if you can't trust your team.
As a military leader, he puts far too much trust in deus ex machina. He was even shown developing a careful battle plan just before the Battle of the Bastards, which he threw away just because Ramsey killed his little brother. He only got out of that one because Sansa showed up with help in the nick of time. Similarly with the Wildlings, who looked ready to kill him just before Stannis showed up to save him in the nick of time. His stupid A-team mission to capture a zombie/walker/living dead thingie from north of the Wall was also about to fail when he was rescued by Dany, again just in the nick of time. That whole mission was something that should have been delegated. It's all great that Jon is willing to lead from the front, but a King shouldn't go off on quests or secret missions. Even King Arthur knew that it was for the Knights of the Round Table to go on the quest for the Holy Grail, and it was his role to stay at Camelot and rule the kingdom.
So nope, Jon Snow ain't my king.
Daenerys Targaryon: Hmmm. She has been learning a lot as she goes along. She's had an opportunity to practice with the Dothraki, with Yunkai, with Meereen and has made mistakes along the way. She has some great qualities in that she is compassionate, abolishing slavery and stopping the gladiator games. She can be ruthless when necessary, but limits her wrath to those who have managed to earn it, taking care to protect those under her rule. She really tries not to repeat mistakes, learning as she goes along. For now I support Daenerys to sit on the Iron Throne!
There are other kings, like Robb Stark, Balon Greyjoy and Euron Greyjoy, but I'm going to shortcut and say that they aren't for me. It's Dany and her Hand, Tyrion for the win!
PS- my position could change again once Season 8 is released next summer. Season 7 already showed some pretty sloppy writing as the showrunners have moved beyond GRRMartin's published books, so I won't be surprised if the story jumps the rails before they bring it to an end.