What do you really need to know about Jaina whenever she is relevant? She is an ice mage that is also in all but name the princess of Kul Tiras. If you want to bring up her relationship with Arthas you mention that they were lovers before Arthas went to Northrend. If you want the Kirin Tor to be a part of it you mention that she trained to be a mage in Dalaran like the rest. If you want her relationship to Anduin you can just say that she cares for him like family.
Kel'thuzad is a disgraced mage that got exiled for practicing necromancy. Thrall is the one that led the Orcs to Kalimdor. Lor'themar is the regent of Silvermoon after their king left/died.
And this is why a dedicated 10-50 questing epxerience is needed. So most of this basic stuff can go unsaid later.