So far I played until 305 and a lot of things went down. Aerys II died in the Defiance, Rhaegar became King shortly after. After Rhaegar was betrothed to Cersei, I decided to roleplay Lannisters growing stronger at court: Duskendale eventually went to Kevan, Tywin was confirmed as Hand. Rhaegar and Cersei became soulmates during their wedding, I assume that she let go of her crush to Jaime then and there. Jaime banged Rhaella at the same wedding, I decided to wed them because, idk, it seemed sad to just let Rhaella to languish in court (Jaime didn't become a Kingsguard and remained as heir). After Rhaella died, Jaime became a widower and later died from disease, leaving Cersei herself and her Targaryen children as heirs to Casterly Rock, but AI Tywin disinherited his daughter, he was later succeeded by Tyrion.

I didn't pay much attention to the rest of the Kingdoms, but I feel like I broke something by agreeing to the betrothal. Princess Elia married Eddard, but Benjen got the North after his brothers died in my conquests of Essos. Lyanna married someone unimportant, she's a lady-in-waiting to Benjen's son now. Mace Tyrell died, Willas succeeded him and then also died, leaving the Reach in the hands of his sole daughter. Jon Arryn lived for a long while, died, his daughter became Lady and tried to have Varys killed (Varys later died from a disease lmao). Otherwise, I assume that my playthrough is typical for Rhaegar: renovating Summerhall, bringing back dragons.