This is a fairly common question you hear with almost any war. I can understand why you would be asking this about Vietnam in particular. It was a rather confusing war even on the ground as far as motivation and goals went. I won't address some of the assumptions you've made in the first part of the question, as they lay outside my area of expertise. The first thing I will address is the Truman Doctrine as you first mentioned.

The Truman Doctrine is incredibly important to why we decided to put ground troops into South Vietnam. Truman declared in 1947 his intent to commit the United States to supporting any nation resisting the spread of "Soviet Communism." There we begin to see the first motivator of US involvement in the conflict and one thing you must realize is that the US began involvement in Vietnam in 1945. So the United States has implied that we are ready and willing to initiate military force against any communist aggressor if deemed necessary. This is important to remember as I will address it once we get closer to the flashpoint of involvement.

We already had a vested interest in the region via the OSI and their involvement with then Vietnamese nationalist Ho Chi Minh. At the time the Japanese were the main threat in the region but as the war wrapped up and the British in tandem with local forces pushed Japan out of the region you then have a loss of a common enemy. The Vietnamese still want their own country, but by 1946 the French had resumed control of their colony and soon after the First Indochina War begins.

The independence movement led by Ho Chi Minh was not originally a communist enterprise. Though it held strong socialist ties, Ho Chi Minh was known even in his later days to be a "Nationalist first and a Communist second." In fact Ho Chi Minh had penned a letter to President Truman pleading for American assistance in gaining independence. He made a direct appeal to our history essentially saying "you escaped your colonial oppressor, we want the same." This letter would never reach President Truman, the State Department did not deem it of importance to forward on to the President. No one in any sort of position of power knew who Ho Chi Minh was. Feeling dejected by the one power he saw as being sympathetic to his cause. Having been educated in Moscow during the 1920s, Ho Chi Minh turned to the Soviet Union and later the People's Republic of China for assistance, thus marking the Viet Minh as a notable communist guerrilla group. In 1946 Ho Chi Minh proclaimed independence from France.

The United States saw this as a dire threat to the Western powers at large. While Truman had no sympathy for an Empire that was clinging onto its colonies, he did fear the spread of communism globally. Vietnam had not been an immediate concern, as you noted the immediate post war activities were wrapped up in Europe primarily to combat the Soviet Union. The real tipping point in South East Asia was the turning of China to communism in October 1949. You then see an almost immediate pivot to the East in US foreign policy as now one of the largest populations in the world at the time was now Communist and threatening Asia. On May 1st, 1950 Truman asks congress to allocate aid to the French war in Indochina to suppress communist guerrillas. Vietnam could be seen as under threat of collapsing under Chinese communist influence. The domino theory held that this was likely, especially since Vietnam shared a northern land border with China. By the final year of the war the US was funding approximately 60% of the French war in the region. Precedent for military involvement would come later that same year with the Korean War.

With communism seemingly stemmed in Korea the French negotiated a peace in Vietnam by 1956. This gains us the partition of Vietnam. With the withdrawal of French ground forces the US sees a threat to the fledgling South Vietnam, which indeed began to immediately see communist infiltration. Thus begins the military advisory role of the United States. Special forces units, military intelligence, and civilian aid organizations began to operate in South Vietnam to ostensibly prevent the spread of Communism. The specter of communism loomed large in the public imagination and indeed there was some economic motivation to this. Ideologically it followed that if South East Asia fell to communism then so to would the rest of Asia and soon it would be on the Pacific coast of the United States. It also meant the closing of markets to US control and participation. Though at the core of this still lies the Truman doctrine and the American ideal that Communism is an evil ideology that must be halted at any cost.

Indeed that cost would come in 1965 when US ground troops begin full military operations in Vietnam. To the soldier on the ground the early years of the war felt like they were repeating Korea. They were going to come in and liberate Vietnam from communist influence and restore democracy. For the government at large this was a necessary move to prevent Vietnam from collapsing under the weight of the Communist North. Though as the war dragged on the US priorities and reasons for fighting the war began to shift. In a March 1965 memorandum to SecDef MacNamara we see the following reasoning laid out for US ground troop deployments:

70% --To avoid a humiliating US defeat (to our reputation as a guarantor).
20%--To keep SVN (and then adjacent) territory from Chinese hands.
10%--To permit the people of SVN to enjoy a better, freer way of life.

ALSO--To emerge from crisis without unacceptable taint from methods used.
NOT--To "help a friend," although it would be hard to stay in if asked out.

It became a matter of reputation for the United States, and this is echoed by Nixon's "Peace with Honor" declaration. Even by the admission of Robert McNamara's closest advisor on the matter, the war was only 20%-30% about keeping Vietnam out of communist hands. By their own admission Vietnam was: "...bad and deteriorating. Even with great, imaginative efforts on the civilian as well as military sides inside South Vietnam, the decline probably will not "bottom out" unless major actions are taken." It began as an excercise in enforcing the Truman doctrine and quickly became about defending the image of the United States as a guarantor of Western Democratic ideals against the forces of Communism.