"There were two good regions for going into Iraq, to stop an immediate WMD threat, or to set up a client state which could help us dominate the region politically and militarily."

Neither of these reasons are good reasons.
If the Gulf War cease fire agreement had not included as part of the agreement for Saddam getting rid of all his WMD, then this would have not been an issue. So the real issue is Saddam refusing to follow a cease fire agreement and the part of the agreement which we considered important was regarding WMD. One consequent of Saddam not following the cease fire agreement was the continuous UN sanctions on Iraq which transformed into UN Food for Oil program. The UN Food for Oil program was very effective in causing Saddam to comply with his cease fire agreement. But had Saddam complied with the cease fire agreement, UN sanctions against Iraq would have ended; and Iraq would not have been invaded.

This situation of Iraq had numerous complications. Saddam over 12 years of time was resisting UN inspectors from doing their task. After Saddam attack Kurds, these Kurds fled to mountains and it was seen by America public as a serious problem, which resulted in America "humanitarian" involvement in Kurd area in Iraq- so this resulted in America having a relationship with Kurds who wanted and considered the Kurdish region as independent country [and this relations began in Bush sr, and continued through the Clinton administration and probably had a lot of CIA activity associated with lots of stuff which not available to the public- but one thing which is known and that is the Kurds really liked our involvement {and perhaps not as liked by the Turks}]. Which btw, that might actually fit an "objective" definition of a client state, so instead "setting up" it would be more accurate to say maintain/strengthen an existing client state.