One key event was Arthas picking up Frostmourne. This was the start of his downfall. Another was his transformation into the Lich King. Also, the creation of the Scourge and his attacks on various kingdoms in Azeroth were important events.
Well, first off, the plague in Lordaeron was a major event as it set Arthas on his path. Then Arthas' decision to go to Northrend was a big deal. When he got Frostmourne, that was a turning point. After that, his merging with Ner'zhul to become the Lich King. His reign over the Scourge and all the destruction they caused. His attacks on places like Quel'Thalas were key. And ultimately, the events leading up to and including his final defeat by the brave adventurers are important in the Wow Lich King story.