Which side are you suggesting we should we have chosen? The al-Sadr killers or the Sunni killers?
Hard to say, but the Sunnis supported Saddam, caused most of the trouble, and since Al Qaeda is mostly Sunni, I’d probably go with letting the Kurds and Shia exterminate the Sunni.
Then they’d probably then fall in with Iran, but that’s an issue for another day.
Of course, then Saudis (Sunnis) would be PO’d, complicating things - another issue for another day - like reminding them that we haven’t forgotten that 15 of the 19, most of Al Qaeda’s money, etc., were from Saudis.