Here's a link to a general outline post I wrote over the weekend on this topic. Always happy to discuss more.

The official stance is that the Warren Commission is correct that Oswald killed Kennedy and acted alone, missing the first shot and landing the following two. However, IIRC the majority of the United States believes otherwise, but no real headway has been made so far to actually disprove the Commission.

Howard Hunt's deathbed confession is interesting, on the other hand. He worked for the CIA, was one of the Watergate burglars, and before he died he admitted to being involved with the JFK assassination along with others from the Agency. But the validity of his confession is in question, as it may have just been the ramblings of a senile old man