Individual experiences will vary greatly, depending on what the service member did, where they did it, and when- great deal of variation along the timeline of the war.
As in all wars, WHY a war began is political, not military. Following WW 2, and getting the Japanese out of the French colony of Indochina (what they called Vietnam then) there were to be elections on a government. Results of the elction were contested, with the resultant division of the country into North/ South.
Equipment will depend again on duty assignments. For Infantry, early on the basic rifle was the M14, later replaced with the M16, and the M79 Grenade Launcher. The M60 Machine Gun (look at the statues at the Vietnam Memorial to see an M60) were used down at platoon level, and 60mm/ 81mm mortars, along with a lot of 105/ 155mm artillery.
Strategically, the war was flawed by the lack of a clearcut overall goal. In WW 2, there was a goal- go after Japan, go after Germany, go after Italy. Destroy their ability to wage war. That was missing in Vietnam. The military was being used by politicians to "send a message".
There are entire bookcases on the subject, not possible to give a simple answer here. Would urge you to look at the men (and women) that were there. Do some research on the Vietnam Memorial- average age, youngest, oldest, average time the deceased had been in Vietnam, branch of service, etc.