The US media were getting a lot of nasty images home, and Tet woke them up to the extent of what was going on.
Winning in Viet Nam means, even without the sudden Tet style wake-up call, that the US public sees a lot more of what the government is willing to do.
Unlike Korea (heavy bombing, no Viet Cong insurgency, WWII style battles) Viet Nam has a major insurgency, it has nasty jungle warfare, it has the US doing all the things it did IOTL Viet Nam except even more of it.
Remember "winning" in Viet Nam still leaves you with adventurous North Vietnamese prone to invasion, a possible resurgence of the Viet Cong, a government that is much worse than the South Korean government, and so forth.
Public relations also depends on which victory scenario we want. Nixon/no Watergate & RFK (see below) probably gets the best press, Diem alive the second best—Tet PR victory and LBJ's second term is probably the worst press.
(A fourth way to win the Viet Nam is have RFK live, win the nomination, win the general, and do Vietnamization faster/earlier than Nixon.)
- Advisors, CIA, special forces, mercenaries (in short, everything aside american soldiers!)
- massive FMS sales starting in 1965.
I'm more interested in aircraft
Certainly as F-4s come into service older planes can be given to the South Vietnamese, but I doubt heavy bombers or top-of-the-line stuff is needed. Without direct American involvement the Chinese and USSR will not engage in quite the one-up competition they did IOTL; the relative air edge of the ATL South Vietnamese might be as large as the US edge was. (Depending more on training than anything else, probably. What would be most useful is Top Gun & Bombing School / South Vietnamese edition.)
As with OTL what matters most is the Viet Cong. South Vietnam, backed by indirect American assistance, can beat the North Vietnamese. However neither South Vietnam nor the Americans can beat the Viet Cong without either a Tet analogue that is equally bad for the insurgency or the really dirty/effective counter-insurgency tactics which means pretty bad PR problems for the US government.