It's not about oil-America has other sources. If by being about oil you mean that Saddam was more trouble then Mugabe because he had oil and thus more money, well that is true enough. But it wasn't to secure oil for America.
It's not about Israel in the sense of America's policies being dictated from Tel-Aviv. While hopefully it will redound to the benefit of Israel as well as to other nations, it was done for our intrests.
As for setting up a Democracy in Iraq, you must remember we don't have to set up a Switzerland. All that really needs to be set up is a government that is reasonably decent for the region and won't cause to much trouble. Any extra is extra.
The war is really about face. A nation's reputation is almost as important as it's actual strength. The politics of nations are like the politics of an undisciplined school, or a prison, or the mafia, or any other system in which there is no generally excepted and well-enforced standard of social behavior. If it is believed we can be hit without getting it back, we will get hit. Which is why it is just as well that Saddam hang. His neck reminded dictators in the region what they are risking if they play with fire.

 Another reason is simply there is no reason not to fight. It is obvious there is going to be a war somewhere in any case and Iraq is as good a place to fight as any.
As for why we are protecting the Sunnis, well they are Iraqi's too, not all of them are insurgents(anymore then all Italians are mobsters), and if they become convinced that there will be a pogram if they submit to the government, they simply won't submit.
As for the "militia's"(I hate it when news people say that-they usually mean "band of cutthroats" which is not what the word originally implied), I have sometimes wondered if we might go a more subtle rout. Some of them are just defending themselves against the insurgents(or general lawlessness) and would be perfectly happy to integrate with the new regime as long as they can be assured of protection. Others are bandits. And others are no doubt betwixt and between. In Vietnam there was a program for organizeing villiage militia organizations under the banner of South Vietnam. They actually performed quite well, though the government distrusted them fearing in the way of authoritarians, that they would owe to many favors to their people.
Something similar organized as an actual auxilery of the Iraqi army might be tried. Of course in practice this will mean local warlords will have to be bribed into becoming , "officers in the Iraqi auxilery forces". But that is nothing new. If a civilization is to be built every powerful person must be either conquered or given an incentive to join in the system. It happened in Europe when barbarian chiefs became dukes, counts, and barons. Something similar will have to happen here. And in anycase those who really are just defending themselves can go on doing so more effectively as part of an organized Iraqi militia, rather then as a "militia group".

 Another reason to protect the Sunnis is a variation of the "Rudy" strategy. Giuliani made a point of arresting petty offenders for two reasons. One is they led to bigger fish. But another was to improve atmosphere. The idea was that if people felt civilized they would be more likly to act civilized while if the neighborhood went to pot it's inhabitants would act accordingly.
Iraq has some similarities to this. At least it is worth thinking about.