First of all, it is a myth that John F. Kennedy was universally loved. In fact, he went to Dallas in November 1963 because be was very concerned about his low popularity in much of that part of the country. He was looking to shore up support before the start of the 1964 election season.
But there are a number of key things about Kennedy that made him different from previous Presidents, at least for the previous 50-60 years.
1. He was inspiring. He had the gift of saying things in a way that made people want to follow him. His inaugural address was one of the finest speeches ever given. If you have never listened to it, you definitely should do that as part of your research.
http://www.americanrhetoric.com/speeches/jfkinaugural.htm
And the inspiring nature of the speech is completely separate from what he actually said. His key line was the famous words, "Ask not what America can do for you. Ask what you can do for America." If a President were to offer the same thought today, he would be hooted down. He would be called "heartless" and "insensitive." He would be totally out of touch. But Kennedy could say those things and still be loved for his leadership. It was a gift, and it touched a lot of what he did.
2. He was young and handsome, and his wife was classy and beautiful. Don't underestimate those things. His two predecessors, Eisenhower and Truman, had been neither, and both their wives had been sort of dowdy. Mr. and Mrs. Kennedy brought grace and style to White House.
3. He was a war hero. Of course, Eisenhower had been a far greater war hero, but Kennedy had been shot at and survived. In a time where there survival of the country was in significant doubt, that counted for a lot psychologically. It is hard for anyone today to regard the Cold War as much more than a period of paranoia, but at the time, it was very, very real. Kennedy was the embodiment of the notion that Anerica could survive and thrive despite the threats all around.
4. This is the big one: He was assassinated. No one alive at that time ever felt the trauma of anything like that. It was horrible and horrifying, and it led to Kennedy being given status as sort of a non-religious "saint." The last President who had been assassinated was McKinley in 1901 (62 years previous). And that assassination occurred before TV and even before radio. For such a tragic event to have played out live was very unnerving for many people, especially since Kennedy was so young and seemingly so vibrant.
As I said, before the assassination, there was legitimate doubt that Kennedy would win re-election. But after the assassination, "everyone" had been for him all along.
Good luck, and I hope this is helpful.