Tough call.
First I should say I've only read through book 4 and only seen up to season 3 of the show. Undoubtedly there are developments I'm unaware of.
I like Tyrion. I mean, everyone likes Tyrion, but I like him for the throne. Having listened to his father and attended high council, he knows politics. Feeling the sharp end of the hate stick all his life has given him a deep understanding of people's capacity for nastiness and great empathy for victims and little guys everywhere. He doesn't suffer fools, even when they're in line for the throne. He shows courage when it counts. He has at least some grasp of his own limitations. He is intellectually astute and has proven he can handle power games. Not only that, he greatly enjoyed his time as Hand, which suggests he won't get too bored with kinging. The drinking and whoring might be embarrassing from time to time but Tyrion would still be an order of magnitude better than Robert ever was.
Jaime Lannister would be a good choice. He's intelligent, skilled in war, and since losing his hand has realized greater virtue almost by the day. His epiphany that he never liked himself and can be a better man than he ever thought spurs him on to....I was about to say nobility, I'm not sure if I'd go that far. He'd have to run a hell of a PR campaign to get past the whole Kingslayer thing, but we the audience know he broke his vow to stop a madman and save a kingdom. If that's not worth compromising an oath, I don't know what is.
Stannis, at first glance, believes in right and law. He also has the best legal claim. On the other hand, he's willing to commit adultery with a witch to win a fight. He is also "the brittle steel that breaks rather than the good steel that bends" or however it's phrased in the books. Basically he's a fanatic. You don't want a fanatic on the throne, even if his obsession is justice. You just know it's going to be that kind of justice: Stannis would create a system of rigid laws, draconian punishments, and omnipotent inquisitors, all hopelessly mired by his inability to understand what the law is actually for. He'll save Westeros by destroying it.
Then there's Daenerys. Passionate, dedicated to good, blessed with undeniable power....but prone to decisions that are morally right but carry onerous consequences. Daenerys is unlikely to provide the stabilizing force Westeros needs. What she will have instead is dragons, which ultimately means a return to the Targaryen policy of ruling through fear.
It pains me to say this but Littlefinger might just be the best choice. He's brilliant, calculating, and ruthless. He doesn't care about people, just money and the long game. This means the economy will flourish, the crown's debts will be settled, and the citizenry will be left almost completely alone as long as their modest taxes are paid. Scheming capitalism FTW.