What affected US military objectives and strategies the most during World War II?
The thing that affected US military strategy and objectives the most in this war was geography.
In this war, American military strategists had to deal with the geographic hand they were dealt. In Europe, this meant that there could be no invasion of Europe for quite some time because the Western Allies were confined to Britain and to North Africa. Until they were ready to mount an amphibious invasion, they could not engage in a large-scale ground war.
In the Pacific, the distances involved and the Japanese control of the small islands between Hawaii and Japan (and Australia and Japan) dictated American strategy. The islands (or at least many of them) had to be in some way neutralized before Japan could be attacked and the war won.