I was alive then. Were you?
Early on, many believed JFK was a victim of conservatives unhappy with his civil rights policy or his policy of appeasement toward Communist countries. This notion was promoted in the media and in books such as Dallas, Public and Private by Warren Leslie (New York: Avon, 1964). This viewpoint is still promoted in books like Dallas 1963 by Bill Minutaglio and Steven Davis (New York: Twelve, 2013). I haven't yet read Nut Country: Right Wing Dallas & the Birth of the Southern Strategy by Edward Miller (Chicago: University of Chicago Press, 2015) but I assume it promotes the same viewpoint.
Many in the conservative media thought that the Soviets or Cubans were behind the assassination because Oswald was a Communist and Jack Ruby had apparently also been one when he was younger. In an article in the John Birch Society publication American Opinion, Revilo Oliver suggested that JFK was killed because he was about to "turn American" and purge the Deep Staters from his administration, withdraw from the United Nations and take a hard line against Communism. A more sober viewpoint is expressed in Carlos Bringuier's Red Friday: November 22, 1963 (Chicago: Hallberg, 1969) which emphasizes Oswald's Cuban connections.
I don't recall hearing conspiracy theories involving the CIA until around the end of the sixties.
This was the first book I read on the subject in the “old days”:
https://www.amazon.com/Rush-Judgement-mark-lane/dp/B0000CN5UV
There were many leads to the CIA presented there (1966)—though I don’t think Lane connected all the dots.
The Israel nuclear nonproliferation issue was not disclosed until Seymour Hersh exposed it in 1991:
https://www.amazon.com/Samson-Option-Israels-Nuclear-American/dp/0394570065
This was a major breakthrough imho since it showed how the CIA/Mossad allies and JFK had opposing views on this topic—which was a critical matter for Israeli security (and US long term security in the Middle East).
While early researchers focused on Cuba, then some later focused on Vietnam, imho the Israeli connection gave the CIA a critical third motive for doing away with JFK.
Fiji — I came to the conclusion years ago that the CIA was involved, not in the murder, but in the cover-up and then framing of Oswald. There were numerous connections between Oswald and various FBI/CIA agents and or operatives (Clay Shaw is one). The CIA actions after the killing was a CYA, because they knew that they looked guilty, not because they actually were guilty.