What were the US's war goals during WWI?

The official stated reason for entering World War I by American leadership was to make the world a freer place. There is no doubt that American patriotism and ideals had an impact on the decision to go to war but we cannot ignore the actual incidents that also led to the decision. The US actually had no interest in entering World War I in the beginning. The American public and politicians wanted to stay out at first. We can say that the US was encouraged to enter the conflict by the developments that took place in 1914 and 1915.

The death of 120 Americans on a British ship destroyed by the Germans in 1915 and the discovery of Germany's plans to cooperate with Mexicans for American territories caused the US to enter World War I.

It was discovered that Germany was trying to get Mexico to join World War I on the side of the Germans. In return, they were promised the territories which they had lost to the US previously. 

These incidents caused a shift in the view of the American public, who eventually supported the decision to enter World War I.

The United States's stated goal in World War I was to "make the world safe for democracy."

By the latter stages of World War I (after Russia dropped out), the war could have been seen as a war between democracies (France and Britain) and monarchies (Germany and Austria-Hungary).  The war could also be seen as a war for freedom of the seas and international rights.  Finally, President Wilson wanted to create a new world order that would make the world more peaceful and more democratic.

In fighting this war, the US gained no territory and got no real tangible benefits.  It was fighting mainly for President Wilson's idealistic view of what the world could be.

What were the United States' goals when they entered World War I?

Nobody expected World War I (1914–1918) to last as long as it did. When it began, the United States's goal was to stay out of it. This was in keeping with the traditional American foreign policy of not participating in European wars. Also, there were millions of Americans with direct ties to nations on both sides of the conflict. However, as the war dragged on, neutrality became harder for Washington to maintain. The US finally entered the war in 1917. What were its goals?

First, we do not know what public opinion was at the time. There were no public opinion polls. At the time of America's invasion of Iraq in 2003, seventy percent of the American public supported the war and the goals of the US government.

According to historian Howard Zinn, there was considerable public opposition to WWI and "over 330,000 men were classified as draft evaders." Zinn believed the real goal of the US in the war was to further its economic interests.

Indeed, the U.S. got into WWI largely because it sought to continue to trade with Europe during the hostilities. Because of British naval superiority, America could not trade with Germany. Britain's fleet blockaded Germany throughout the war. America could, and did, maintain commerce with Britain and France, though. Trade with the Allies became increasingly important to the American economy as the war progressed. In 1915, a German submarine sank the Lusitania, and over one thousand civilians—including over one hundred Americans—were killed. Germany stopped its wide use of submarines until 1917. Then, the now-desperate Germany resorted to unrestricted submarine warfare, and America entered the war.

President Woodrow Wilson put forth his "Fourteen Points" as America's war goals. These included "freedom of the seas" and other idealistic goals. However, most of his "Points" were never implemented. America's European allies and the US Senate never accepted them. After the war, the US went back to isolationism.

You are right when you state that the idealistic Wilson wanted peace between all countries. That peace was supposed to be maintained by the League of Nations. But the US Senate would not allow America to join the League after the war.

President Wilson dragged a reluctant country into World War I after Germany stepped up its submarine attacks on U.S. vessels in an attempt to cut supply lines from the United States to the Allies for long enough to win the war. The Germans calculated their renewed assault in early 1917 would bring the U.S. into the war, but also reasoned that they would have won the war by the time the U.S. mobilized.

Though the U.S. public was largely wedded to isolationism, and Wilson himself agonized over the decision, he felt the time had come to do something about the European situation. He, of course, wanted to defeat Germany, but he had a larger vision and hoped that by entering the war, the U.S. would have much greater influence on the subsequent peace process. He outlined four goals: larger and smaller nations (by which he meant more powerful and less powerful) being treated equally, the creation of an international association to mediate conflicts (this would become the League of Nations and later the UN), the end of nations trying to grab territory from each other, and the end of the private arms trade, which encouraged companies to support war for profit. In other words, Wilson paradoxically entered the war to try to end wars: this was the "war to end all wars." 

Wilson, along with the American public, felt that going to war was both necessary and wise for a number of different reasons. The overwhelming reason was that the war was crucial in order to make the world safe for democracy. The U.S. believed that it had a strong devotion to both freedom and democracy, and that the sooner the rest of the world accepted those principals the better. Entering the war would help foster democracy in other nations by blunting the power of more aggressive, imperial nations like Germany and the Ottoman Empire.

Underneath this veneer of moralism was a more practical goal. The U.S. had loaned large amounts of money to the allies, and if they lost those debts might not be repaid. Financial security was also a chief goal for the U.S. upon entering the Great War.

Also, the German military decided to allow unrestricted U-boat warfare as the war continued, and soon the U.S. was losing ships as they crossed the Atlantic. Protecting shipping became another chief goal of the U.S. during World War I.

Another aim was the security of its own borders. Germany had sent a proposition to Mexico that asked the U.S.’s southern neighbor to join forced with Germany in exchange for territorial rights that Mexico had long claimed after the Mexican-American War. Hoping to end future allied proposition, the U.S. entered World War I.