Matewis: Never payed too much attention to the W2 campaigns back then (ie the story), but I'm looking forward to doing so for this playthrough :)
I would say the story in Warcraft 2 is pretty well told. It's not very original or engaging but it gives you a good amount of information where you are and why the task you got is so important. You are fighting a few battles in the whole war but you learn why they are so crucial. So yeah, I encourage you to follow it.
Matewis: I have to admit though that I kinda lost track of who the 'bad guys' were in the Frozen Throne at some point - Illidian and the Naga threw me off a bit :P
The answer is: all of them ;) Sure, Arthas is probably the worst but both prince Kael'thas and Maiev Shadowsong have a good share of terrible deeds. Sure, they have a good justification why they did what they did but actually Arthas can claim it as well ;)