Eisenhower was the first to send military advisors to South Viet Nam, not JFK.
JFK is famous, not for increasing the number, which he did, but for reacting to the book “The Ugly American” by requiring special training for the Special Forces that included good deeds with the anti-Communist South Vietnamese.
LBJ is famous for giving the war to McNamara and the whiz kids who had no clue. They undid everything JFK intended by sending us 550,000 guys over there with no training of any kind.
So far, I have not seen an accurate history of the war from either left or right. The closest thing to reality is a couple paragraphs in Susan Brownmillers “Against Our Will”.
But ultimately the war was lost by the incompetent South Vietnamese government, who could never rally their own population to the degree that it needed to be to defeat the North.