The easiest is probably a vanguard trooper specced as assault specialist. The skill rotation is very simple and strong and you get your healing companion pretty early. The story is good as well.
The smuggler story is the funniest in the game. A dps scoundrel has stealth and a simple rotation as well. You don't get your healer comp until. 4/5 of the way through.
That's it right there. Although you can solo more content if you play a healer character.