Our military presence in Vietnam was not the result of a single policy or objective by any person or administration, but rather an outcome of political involvement spanning over many administrations and ideals.
Before we were ever involved in Vietnam, it was a victim to French imperialism. The French rule over this Far-Eastern colony induced small rebellions aimed at freeing the Vietnamese people so that they could become an independent state. Perhaps the most important of these rebellions was led by a group in Northern Vietnam called the Viet Minh, whose leader was known as Ho Chi Minh. He organized the Viet Minh around 1941 after living thirty years in exile, traveling all over the world, and grasping communistic ideals.
At that time, a primary US interest was the elimination of imperialism. Franklin D. Roosevelt particularly promoted this idea and it was one of the results he planned on seeking once World War II ended. At the same time, Japan, an enemy of the US, had moved into parts of Vietnam and was battling the French for control. Given these circumstances, the US actually supported Ho Chi Minh and his rebel group became a key player in ousting Japan from the territory.
With the end of the war and the unexpected death of President Roosevelt, a number of circumstances changed which eventually induced our military involvement in Vietnam against Ho Chi Minh and his allies. Two main factors of the change were the liberation of France in 1944 and the role which they were permitted to play in the defeat of Japan. These both led to an "ambiguous" policy on Vietnam due to the position in which US was trapped - whether to continue giving aid to Ho Chi Minh in his endeavor for independence, or to side with the French and allow them to retain their colony.
By 1947 the French had instigated an attack against the Viet Minh and war had commenced. A new anti-communistic foreign-policy by the Truman administration resulted in a pledge of American support to the French, but over the next several years the French suffered losses against the Viet Minh for which the French government finally decided to remove itself from the territory. By this time President Dwight Eisenhower was in office and the United States was taking a powerful stance against communist countries, moving our interest in a non-communist Vietnamese government to a top priority.
The US helped organize a Southern Vietnamese anti-communistic government and commenced in giving them aid and training in order to fight the Democratic Republic of Vietnam. This effort proved fruitless over the following years while US interest only increased in South Vietnam's success due to a belief in the "domino effect." Not until 1965 were the first US ground troops sent to Vietnam under the Johnson administration.
The above shows us that many domestic policies and international factors played a role in our ultimate conflict with Vietnam and the war cannot be blamed on any single individual or administration.