In the USA we saw the Vietnam War as a proxy war against the Soviet Union and/or China, a battle of ideologies. I know that the Vietnamese saw it instead as a war of independence and liberation from European influence. But how do they contextualize it within their broader history, e.g. with relation to China? Is it something that starts with Ho Chi Minh or does it go back much further for them? Is the Communism aspect essential to how they see it or incidental?
I feel like you generalize the views of the Vietnamese to the extreme. First, we have to understand that there was a large difference in views between the North Vietnamese and South Vietnamese in this matter. The North Vietnamese government made out the conflict to be that of a war of liberation. Young men were conscripted into the People's Army of Vietnam and told that they were going south to liberate their brothers from the shackles of imperialism and reunite Vietnam under one banner. For those in the North (and those who supported the northern view of the war in the south), the government (i.e. communist) aspect was essential and always had been. This was a carry-on from the dau tranh of the Indochinese War which was meant to mobilize the population for war.
Then we have South Vietnam which was an independent nation and who for many was a better alternative than communist North Vietnam. Plenty of farmers had fled North Vietnam during the mid and late 1950's and had no desire to fall under the same regime once more. Plenty of others found themselves in the same boat as the US view, seeing the fight against communism as fighting for their freedom. The South Vietnamese government carried out plenty of policies that would damage its reputation in the long run (besides being a dictatorship), but we can not forget this essential aspect to a very complex conflict.
However, the American War (The Vietnam War) was seen as a continuation from that of the Indochina War. This whole sequence is usually put into context with the Vietnamese anti-colonialism and independence movements of the late 19th century and early 20th century. Essentially, it is tied with Ho Chi Minh. If we want to take a broader look at it, some definitely do put it into context as yet another conflict in which Vietnam has fought against foreign invaders - quite commonly with asymmetrical means as well.
Northern Vietnamese: Many were made to believe by the NV govt that the conflict was to liberate the south of the invaders (America and her allies). During 1954 to 1956, however, about a million northerners fled to the south because of the common belief that the south was more well-off (and it still is to this day).
Southern Vietnamese: Quite a number of folk were in the same boat as the majority of northerners in believing that South Vietnam was being invaded and held as a puppet state for the foreign 'imperialists' (America and her allies). However, the majority simply felt that their livelihoods were being threatened.
Modern day Vietnamese: The war is taught as one of conflict against the imperialist Americans who tried to keep the brothers and sisters of Vietnam separated from one another. Ho Chi Minh is idolised as almost a deity of sorts. They are taught that he was a gentle soul, the man who loved his nation above all others and tragically died before being able to witness the glorious 'liberation' of South Vietnam. This is quite ironic given that the US and all things American are admired by much of the younger population.
Overseas Vietnamese/Việt Kiều: Most of the older folk are obviously people who had first hand accounts of the war and are extremely biased against the communist govt. They regularly hold protests and fundraising events for the veterans of the war. They also fund the building of monuments dedicated to the boat people legacy. My mum often recalls of times when the area around her high school was constantly being shelled and of how her father was imprisoned unjustly for several years just for being accused of helping people escape the country via boats.
Personally: I find the war to be a huge waste of lives, money and time. An estimated 3 million people died as a result of the conflict and hundreds of thousands of others died at sea in the search for safety and freedom in distant lands. I do admire the desire for independence from France expressed by Ho Chi Minh but beyond that his actions either directly or indirectly led to the suffering of too many peace-loving folks.
The war led to famine, disease (including birth defects from harmful chemicals used), environmental destruction, a severe collapse and stagnation of the economy, the exodus of a million people including many intellectuals (which spurred on a refugee crisis) etc...
Source: I'm Vietnamese, have read a lot on the war on both sides and have heard a lot of stories from older folk including my own parents.
Depending on who you are talking you the Vietnamese have diverse opinions on the war and it's reason, and the state of their country afterwards. War is awful in a lot of ways and regardless of ideologies people will not look back on death and destruction in a positive manner--many people lost their families, homes, and way of life. I would recommend checking out the documentary "Oh, Saigon" to get a small glimpse into the differing opinions of a multi-generational Vietnamese family. The recollections of the war range from misery to deep humiliation to freedom through communist philosophies, and all these views are colored by their actual personal experiences and sufferings during the conflict. Very good documentary.