Warning! There are a tremendous number of SPOILERS in my post.
Sy, as Stannis told Davos, it's not about whether someone wants to be king... it's about rights of inheritance. So is the conversation about anyone or only those from the Baratheon line of succession? It seems you'd like to include powerful lords in the discussion as well. I'm up for all of it...
But what makes a good king? I think we know the obvious traits that define a bad king. But what defines a good king? What should the Seven Kingdoms look like under a good king? Financial prosperity? National peace? Civil justice? Access to education? Lower taxes? Freedom of religion? Free speech? Abolition of slavery? Building the Wall? Free market economy? Bigger or smaller military? Healthcare?
Upon Robert's death the Seven Kingdoms were brought into another age of the Game of Thrones. Joffrey, Stannis, and Renly all claimed the throne for themselves. Joffrey and Renly are dead. Tommen has taken Joffrey's place while all of Renly's power was divided amongst Stannis and the Lannisters. Robb Stark and Balon Greyjoy proclaimed themselves kings of independent realms, yet both of them are now dead. The Kindom of the Iron Islands is now lead by Euron Greyjoy... with a possible minority under Queen Asha Greyjoy, but this is not definite... and the Kingdom of the North and the Riverlands might have completely dissolved back under Lannister leadership... with a chance that Robb's wife, Jeyne, is pregnant. There was also an unsuccessful coup attempted in Dorne to make Myrcella Baratheon Queen of the Seven Kingdoms. And the realm survived two potential invasions... one by Mance Rayder, King beyond the Wall, and one by Khal Drogo of the Dothraki. Drogo's plan was to seat his son upon the Iron Throne... his son by Daenerys Targaryen, daughter of the king deposed by Robert. Dany is still out there being courted as an ally or outright queen by both the Greyjoys and the Martells... if not also Lord Baelish, Lord Varys, and the Tyrells. Lord Baelish might also have a plan to form a breakaway combined Kingdom of the Vale, the Riverlands, and the North. But he most likely seems to be planning to rule the entire Seven Kingdoms as the power behind the throne. Oh... I almost forgot Aemon Targaryen. As a the eldest surviving son of King Maekar, Aemon was offered the crown once upon a time... Dany is his brother's son's son's daughter. But mayhaps his brother's son's son's son's son is still alive... his name would be Aegon... VI.
Did I mention everything? So who are the candidates as monarchs in this topic of "Who do you think would have been a good king of the Seven Kingdoms?
Assumed Baratheon line of succession: Robert, Joffrey, Tommen, Myrcella, Stannis, Shireen, Renly.
Actual Baratheon line of succession: Robert, Stannis, Shireen, Renly.
Public Targaryen line of succession: Viserys, Daenerys.
Hidden Targaryen line of succession: Aegon, Viserys, Daenerys, Aemon.
Royal bastards: Gendry Waters, Edric Storm, Mya Stone.
Potential royal bastards: Jon Snow, Bella Rivers.
House Arryn: Jon, Robert.
House Greyjoy: Balon, Euron, Victarion, Aeron, Asha, Theon.
House Lannister: Tywin, Cersei, Jaime, Tyrion, Kevan, Tygett.
House Martell: Doran, Arianne, Quentyn, Tristayne, Oberyn.
House Stark: Eddard, Robb, Bran, Sansa, Arya, Benjen.... Robb's unborn son.
House Tully: Hoster, Edmure, Brynden... Ed's unborn son.
House Tyrell: Mace, Willas, Garlan, Loras, Margaery.
Others: Littlefinger, Varys, Jeor, Mance, Tormund, Roose Bolton, Jon Umber, Lord Farwynd, Erik Ironbreaker, Dunstan Drumm, Walder Frey, Black Walder, Randyll Tarly, Mathis Rowan, Alester Florent, Axell Florent, Kevan Lannister, Khal Drogo, Khal Ogo, Khal Pono, Khal Jhaqo, Illyrio Mopatis...
I think this is a fairly comprehensive list of claimants, lords, powerful people, leaders, office holders, and capable men. I'll leave listing the qualities or vices of each of these characters for a later date... or for everyone else.