I think if you're new to the whole idea, I would go with 2 of the same class. It will streamline many things for you until all the mechanics are second nature.

Ideally, 2 ranged dps classes that can heal and rez would be ideal to start with: shammie, druid, priest. I'm not saying that those are the best duo teams, just that there will be less micromanagement, they share class specific quests, quest rewards etc. Any team of 2 will roll through single player content without issues.