We went into Iraq because it was the most logical target.
The September 11 atrocity was planned and financed by bin laden and al qaeda. Their money and people came mainly from Saudi Arabia and Afghanistan, with the Afghan government (the taliban) being the most overtly anti-American and belligerent. Afghanistan also gave aid and shelter to the mastermind, bin laden. For this reason alone, they became target number one.
The pentagon knew that Afghanistan was too distant a target to make a truly effective demonstration of their new resolve against terror, so another target had to be chosen. The country that deserved it most was Saudi Arabia, but since they have been a "friend" of the U.S. for so long, there was no way we would attack them. Besides, I am sure that they have bankrolled a large portion of our activities in Iraq - trading money and oil for us to not invade them...
Though I don't buy into the War for Oil propaganda, if you are going to choose a country to attack, you should choose one that makes the most sense. These were the criteria for the countries that were considered for invasion in order of importance:
The country must be mainly islamic and located in the Middle East.
The country must not be too strong militarily or financially.
The country must have mediocre to poor relations with other islamic countries.
The country should have oil.
The country should have a secular government (for ease of transition to democracy).
The country should have a tie-in to terrorism (most of them do...).
It really didn't matter which islamic country we attacked. It was more important that we not back down again like we had under Clinton. We had to make a stong showing in the back yard of the islamic fundamentalists. Their extremist religion knew no national boundaries, so what difference should boundaries make when choosing a nation to invade?
Iraq fit the above criteria best. It had the added advantages of being the other bookend to Iran, having its air space already under de facto U.S. control, and it was still being run by Saddam Hussein who continued to be a burr in the Bush family's saddle.
Even if Iraq had nothing to do with September 11 (and they probably didn't) they were the most logical target for the reasons outlined above. Larger wars have started over less.
-Dave