If you're looking specifically for battles, I recommend "With the Help of God and a Few Marines" written by Albertus Catlin and Walter Dyer. It was written in 1919, fresh after the war by one of the commanders of the US Marines at Belleau Wood. Solid, on the ground view that hasn't been tainted too much by time and the inevitable romanticism that creeps in for important battles or events. There will be some, or course, but it's as close to a comprehensive primary source as you'll get for an American troops view of the war.

Broader views and books on how and why America got involved, I'll leave to others.

I recommend Michael S. Neiberg's recent book The Path to War: How the First World War Created Modern America . It's a readable history of the lead-up to America's entry into the conflict and argues against the traditional view that the US was dragged into the war by Woodrow Wilson and bankers, with Neiberg instead showing how by 1917 the bulk of the American population was eager to get into the fight despite the reluctance of their politicians.