Read through the manual, especially the nine (!) pages they devote to the plot in teeny tiny text. For a newcomer it's extremely confusing. The Zerg make sense, but the constant shifting of Terran allegiances and Protoss character names make my head swim. IGN's five minute video summary helped, though I had to watch it three times.
I take it Kerrigan is the anti-hero everyone loves, vaguely like FFVII's Sephiroth. And there appears to be some slight debate as to whether there's any humanity left in her, though her temporary alliances appear to be more for strategic convenience than any real compassion.
What I'd like to know from my fellow HN gamers is the emotion of it. What were the shocking moments? The tearful bits? Were there any? What would I feel about Jim Raynor if I played through Starcraft and Brood War? Am I supposed to think Kerrigan as the Queen of Blades is sexy, or am I supposed to be repulsed by the... things growing out of her back?