TL;DR at the bottom.
Many criticize Renly Baratheon for taking a claim to the throne but often don’t consider what would have happened if he was successful. The two major talking points I’ll be talking about are why Renly becoming king would have been the best scenario and why he would was the best candidate out of the 3 kings who wanted the Iron Throne.
Why Renly becoming king would have been the best case scenario for Westeros
To start out, let’s look at the scenario that did happen with Renly having died by Stannis’ shadow child. Robb Stark was unsuccessful and died in the Red Wedding, Stannis failed to take King’s Landing and died at The Battle of Winterfell, and the Lannisters won The War of The Five Kings with Joffrey sitting on the Iron Throne with Margaery Tyrell at his side. The war went on for years, thousands died, the Stark family was devastated, Westeros is destroyed, the legitimate Baratheon bloodline was gone, and the Lannisters had power over Westeros.
Renly died with 4/5 of his army aligning themselves with the Lannisters after his death, Stannis states Renly’s bannermen except for the Tyrells sided with him. According to the wikis, 20,000 of Stannis’s army was from Renly, and Renly stated to Caitlyn that he had 100,000 men at his command, making the Tyrell contribution to his army 80,000.
Many people say Renly should have supported Stannis’ claim and gotten the Tyrells to join Stannis, but miss the point or motivation behind the Tyrells backing Renly then backing the Lannisters after Renly’s death. The answer is simple: they wanted power through Margaery becoming queen. If you look at the bathtub/shaving scene with Loras and Renly then the attempted sex scene with Margaery and Renly, it’s quite clear they were trying to gain power through him making a claim on the Iron Throne, even before Joffrey and Tommen were known bastards.
So quite predictably, the Tyrells sided with the Lannisters after Renly’s death since they wouldn’t be able to marry Margaery to Stannis, but Stannis didn’t have the people knowledge to guess why the Tyrells sided with Renly. Since the Tyrells sided with the Lannisters after Renly’s death, Stannis failed to take King’s Landing, Robb Stark failed at creating an independent North, and Joffrey sat on the Iron Throne when all was set and done.
But what if Stannis hadn’t killed Renly? What if Renly had crushed Stannis’ army the next morning then took King’s Landing? If that had happened, he would have had 100,000 or so men at his command to take King’s Landing, more than 4 times the army Stannis used, and about 3.6 times the Lannister army and King’s Landing garrisoned soldiers combined. Lannister reinforcements wouldn’t have been able to reach them in time with the overwhelmingly more soldiers Renly had, and even if they had, Renly likely would have still won due to sheer numbers.
So Renly takes King’s Landing, Joffrey’s head is on a spike, and Renly sits on the Iron Throne, what now? With the Lannister army either devastated or away from King’s Landing, Renly would be able to help Robb defeat them, and create a pseudo independent North and the war would come to a close. The Stark family is alive and strong with a pseudo independent North and no Red Wedding, the war ended in one year instead of five, Westeros isn’t a ruin, the legitimate Baratheon bloodline is alive and strong, the Lannisters are dead, and Westeros has a king they love.
It’s clear that Renly becoming king would have been the best scenario for Westeros, yet Stannis dragged out the war for much longer than it needed to with catastrophic results by killing Renly.
TL;DR: Renly dying resulted in the Stark family failing and dying in the Red Wedding, Stannis failing to take King's Landing, Lannisters having power, Westeros being a ruin, and the war going on for 5 years. Renly not dying would have resulted in the Stark family being successful with no Red Wedding, a successful siege of King's Landing, Lannister family being dead, Westeros being mostly in one piece, and the war ending within a year.
Why Renly would have made a better king than Stannis or Joffrey
-People loved Renly far more than Joffrey or Stannis.
People loved Renly, that’s why everyone went to him instead of Stannis while Stannis was only able to muster up 5K men to fight for his cause. Stannis is an incredibly unlikeable person and not one who’s able to inspire love or loyalty as many characters have stated in the show. If we look at the books, Stannis is so unlikeable that even his brother in law sided with Renly.
Joffrey was hated by his people as well, there were riots while he was king and when someone threw a mudpie at him, he ordered his guards to start killing people. He bullies his people with his sadistic ways and make them fear him instead of love him. If we value what the people want and what would be best for them in any way, it’s clear Renly would have been best fit for the job.
-Renly was a far better diplomat than Stannis or Joffrey.
The biggest example of the diplomatic difference between Renly and Stannis is the handling of Robb Stark wanting to be the King of The North. Neither wanted to lose half of their kingdom when they became king, so what do each of them do? Renly offers Caitlyn a pseudo King of The North title to Robb, as long as Robb swears an oath of fealty to him, citing how Baratheons and Starks have had a long and prosperous history working together. Pretty good, right? It leaves everyone happy and does bring up a good point of them working together in the past being massively successful for Westeros.
How does Stannis reply to Robb Stark wanting an independent North? In the scene with Renly, Stannis, and Caitlyn, Stannis complains about Caitlyn being next to Renly then stating to her about Robb Stark: “The Iron Throne is mine, by right. Anyone who denies that is my foe.” He doesn’t ask if Robb is actually interested in the Iron Throne or just an independent North like Renly, doesn’t offer a possible solution or compromise that would make everyone happy like Renly, instead he gets upset at Caitlyn and digs his feet into the ground even deeper, blinded by what he thinks is his by right.
Is that the kind of king who would be best for dealing with situations and conflicts that come up between his seven kingdoms? No. The best king would be the one who comes up with a compromise and solution that everyone is be happy with, such as Renly did with Robb Stark.
Joffrey doesn’t handle people well, that goes without saying, from starting riots due to killing people, to holding Sansa at crossbow point because he’s bored, to being an overall cruel king. Any diplomacy done is either fucked up by him, or completely manipulated by Tywin Lannister who only has his legacy’s best interests at heart instead of everyone’s.
-Renly is the most progressive of the three kings who wanted the Iron Throne.
Renly does what is just and fair, without caring if it’s socially correct or the norm, which is why he made Brienne part of the Kingsguard as she had wished. Stannis is incredibly socially conservative, banning brothels in Dragonstone and is a religious fanatic, burning people alive to gain favors with the Gods. In the scene with Joffrey and Margaery, Margaery talks about Renly wanting anal sex and Joffrey acts disgusted and claims he has been thinking about outlawing it, despite it not hurting anyone.
From these few examples, it’s clear that Renly is the only one of the three that looks to what’s right, not the way things are “supposed to be” or what they feel grossed out by.
-Renly is the only one of the three who hasn’t done cruel things.
The worst thing Renly had done was claim he’d be the best king against an illegitimate bastard and a brother no one wanted to be king. What’s the worst thing Stannis had done? Burned his nonbeliever brother in law alive, used blood magic to kill his brother, nearly choked Melisandre to death because he was frustrated, tried to kill his nephew as a sacrifice until Davos was able to convince him otherwise, burned his daughter Shireen alive in front of his army, and led to his wife hanging herself.
A king who resorts to burning loved ones alive for good luck from the Gods has no business or suitability being king. He’s a stubborn fanatic whose blinded by his religion and what he thinks he deserves, without any regard for those it’ll harm or what’s the best scenario for people.
There’s a laundry list of cruel things Joffrey has done, but off the top of my head: abused and killed prostitutes, held Sansa at crossbow point because he was bored, had someone’s tongue cut out or his hands cut off because he didn’t like the song, nearly force drank someone to death, and abused Sansa.
TL;DR: Renly becoming king would have been the best case scenario for the Starks, Westeros, and everyone except for Stannis and the Lannisters. Renly was the most loved, the best diplomat, and the most progressive of the three who wanted the Iron Throne, and isn’t cruel like Stannis and Joffrey were.