How did Ner'Zhul conclude Arthas is the best person to become the Lich King?
I was playing Warcraft III: Reign of Chaos many years ago; so I have forgotten some plot points.
When Arthas was killing the plagued people of Lordaeron in order to kill Mal'Ganis, he suffered a severe headache and the ghost of Ner'Zhul started communicating with him to instruct him to go to Northrend.
Mal'Ganis himself was there to instruct him the same.
What factors led the bad characters to think that Arthas is the best person for them?
There is a lot of speculation surrounding this topic, even dating back as far as Wrath of the Lich King, but not much fixed lore. However, from recent events in Shadowlands, it appears that both Ner'Zhul, Arthas and (lately) Sylvanas are controlled by The Jailer, the primary antagonist of Shadowlands. In a recent quest in Shadowlands, it appears that the Lich King was meant to herald the entrance of the Jailer, and that the Dreadlords (the Nathrezim) are also part of the Jailer's forces.
Purely based on Warcraft 3 elements though, most speculation focuses on Arthas having a single minded focus on wanting to save his people, and it might be this singular drive to do whatever it takes to fulfill his goal that made Ner'Zhul choose Arthas. Again, it's likely that Shadowlands is going to explore Arthas and the Lich King more in depth in the coming patch cycle. Blizzard has already confirmed in an interview between Steve Danuser and community figure Bellular that we're going to see more of Arthas and Ner'Zhul in upcoming patches.