A JFK specialist may come by, but my understanding is that JFK himself was very pro-Israel, though with some caveats.

To understand that, I did a bit of digging into his past. What's interesting is that in 1939, he wrote a letter to his father. The letter was mostly descriptive, and even seemed to favor the Palestinian stance. The young JFK, just about 22 years at the time, claimed that "the Jews have had, at least some of their leaders, an unfortunately arrogant, uncompromising attitude...". This belief clearly changed following the Holocaust, as well as the period of the UN attempt to form a partition plan. Interestingly, as you can see the letter was written to his father, who apparently was a horribly anti-Semitic person who worked with Charles Lindbergh and wanted to ship German Jews to Africa.

Following the passing of the UN partition plan of 1947 (never implemented), another document of note that I found is this. The writings are notes on a speech JFK gave in April 1948. At this time, civil war was raging in the British Mandate, and Truman was appearing to reverse his position in favor of partition. The US had placed an arms embargo on all sides in December 1947, but this practically meant that the Jewish side was the one most unable to get weapons, since the US continued to fulfill contracts already signed to supply Arab states (who then funneled weapons and "volunteers" into the civil war, before invading in May 1948). JFK was a member of the House of Representatives at the time, and the notes indicate that he called it embarrassing to see the partition reversed, and also called on an end to the embargo. He said ending the embargo was necessary, "to give the Jewish people in Palestine an opportunity to defend themselves and carve out their partition".

JFK continued to be pro-Israel, and his speeches as President affirmed that. He spoke glowingly of Zionism, of its modernizing effect on the land, of its creation and its right to "endure and flourish", etc..

However, President Kennedy was not always glowing about Israel. One of the biggest points of contention for him was Israel's nuclear program, and the possibility of nuclear proliferation. Recent documents reveal that Kennedy and Israeli Prime Minister David Ben-Gurion met and discussed Israel's nascent nuclear program, and while Israel hinted at possible plutonium production, it claimed that there were no intentions to produce nuclear weapons, though there is dispute as to whether that was explicitly said. At any rate, it was clear that Israel was not being truthful in this case. I'd be remiss if I didn't mention that back in these days, nuclear proliferation was seen as a threat but there was no Non-Proliferation Treaty as there is today, which came into force in 1970. Even so, JFK was not happy with Israel's development of its Dimona nuclear plant, which was perhaps the biggest source of tension.

Despite this tension, Kennedy viewed Israel as a strategic ally and a pro-democracy one at that, and as such extended the first security guarantees to Israel by an American President, and sold advanced weaponry to Israel. This paled in comparison to the support of later Presidents, but JFK was definitely a shift for his time.

At this point in time, Palestine had not declared any kind of statehood. The Palestinian Liberation Organization was not yet founded, and wouldn't be founded (as an Egyptian proxy of sorts at first) until 1964, after JFK's assassination. Fatah, which today runs the PLO and the Palestinian Authority and has since 1995, was not founded until 1965. Palestinians and Palestine were not a "thing" for JFK to consider. Back then, the conflict was seen purely as an Arab-Israeli one. It was following the peace with Egypt that the conflict was redefined to be "Israeli-Palestinian" in large view, since Arab states no longer seemed to be willing to take up the mantle of the Palestinian cause with weapons and wars. So JFK may not have thought much at all about "Palestine" or Palestinians. Indeed, the occupiers of the West Bank and Gaza at the time were Jordan and Egypt, respectively, rather than Israel, though Jordan actually annexed the West Bank (which went unrecognized). If I find something additional while digging later, I'll add a separate response.