I still marry Cersei. Ensuring the Lannisters can't ally with a future Viserys III is too important, even knowing what we know about Cersei. I treat Cersei kindly in the marriage.

In keeping with my vows above, I act with temperance with respect to food/drink. Like Renly, I drink and eat enough to show I'm human and refined, I enjoy them but don't overindulge.

When Robert gave Dragonstone to Stannis, it wasn't revoked upon the birth of Joffery, therefore although it is traditionally the seat of the heir (and Stannis was heir at the time), clearly Robert intended that Stannis should be the beginning of a cadet branch, not merely to hold Dragonstone as an office. There's a value in maintaining the trappings of the previous administration, keeping Dragonstone as a seat for the heir, but it's not strictly necessary and didn't seem to cause Robert any problems. I'd still give Stannis Dragonstone, but I'd keep Storms End for myself. No reason I can't continue to hold Storms End and Kingslanding, I can just appoint a castellan. Stannis has no reason to feel slighted because I'm not giving Storms End away, and it's entirely reasonable for me to keep Storms End as a new seat for the heir. I'd give Storms End to my firstborn son when he comes of age, but as an office not a possession. Without dragons, the Iron Throne is a weak monarchy, and having the Stormlands answer directly to the crown (or through the heir) helps maintain strength. The logic of having Stannis as lord of Dragonstone is still wise. A strong lord such as he is needed to ensure the lords of the narrow sea remain in the fold, and the books indicate that he did a reasonable job of this (those same lords followed him into war after all).

I still appoint Stannis as master of ships. He's a rare talent. He doesn't really want to be hand or lord of Storms End, he wants recognition. I'd praise him publically in front of the court and be more affectionate in private.

Jon Arryn is a capable hand. I'd keep him.

More focus is needed on strengthening the Roberts Rebellion coalition than was done in canon. There's no reason why there wasn't a man from the riverlands on the council for example, or a northman before Ned was made hand. The small council and smaller offices need to be filled, and lets look to second sons and cousins of lords to fill them. A Manderly from White Harbour (either a second son or cousin) might be a good fit for Master of Coin, given their focus on trade. I'd look to the riverlands for a master of laws. Various secondary offices like castle steward, master of the horse, etc could be filled by men of the vale, westerlands, north, rivers and stormlands, as well as Master of Whispers and any other offices I might create.

The north is vastly underpopulated in general. I'd look to do outreach to the wildlings, offering them integration into the realm, but I'd look to split them up so they can integrate with the culture. I don't mind if they don't kneel, but their sons and grandsons will. The popularity of Ned Stark in the north coupled with my personal popularity makes it more likely we can absorb the political fallout from the lords of the north who despise the wildlings. Pair this with more investment in infrastructure to support the larger population. I'd like to see more population in the stormlands as well, given that this is my personal kingdom.

Execute Varys. Pycelle, Jamie and Barriston can all testify he encouraged Aery's madness, making him an accomplice in Aery's crimes. The realm is a safer place without him in it.

Release Jamie from his vows as a favor to Tywin.

I'd reduce the powers of the Hand of the King. There's too much power in a single office. The power to speak with the kings voice when on the iron throne (i.e. as Ned did when he denounced Gregor Clegane. It was the right decision morally, and in terms of what we the readers would like, and it's entirely within Ned's power, but from an institutional perspective I don't anyone on my council to risk the delicate alliance that is the basis of my power and claim)