During his time as a Congressman and Senator, JFK developed a philosophy concerning advisers that went something like this: He would surround himself with quality people as advisers, get various points-of-view, and then make a decision on his own. JFK viewed advisers as essential, but he thought their POVs should always be viewed with some skepticism - he was determined to never be a captive of any individual adviser or group of advisers. Also, he wanted his advisers to "compete" with each other for access and influence, something he learned from FDR. Even before his presidency, multiple advisers competed for his attention, but in the end, JFK only truly trusted his family - his father, and his brother, Robert Kennedy. Despite his philosophy, JFK didn't become the "Decider" that he envisioned until after the Bay of Pigs debacle just months into his presidency in 1961.
LBJ should have had the nomination in his back pocket, but he waited too long before he formally announced his candidacy; by then, JFK had a great head-start in terms of committed delegates for the convention. Hubert Humphrey was a different story, in that he started early like JFK, but he also started early with "dirty tricks". Among the political shenanigans used by Humphrey were accusations that JFK's health was a mess (which was true), and he also played the "Catholic Card" trying to scare voters to head his way. RFK's response to Humphrey's strategy was two-fold: respond with "dirty tricks" on their own, and also raise more money than Humphrey, which was a fairly easy thing to do since their father was worth over a billion dollars (adjusted for inflation).
At the Democratic Convention in the summer of 1960, JFK offered LBJ the Vice-Presidential slot on the ticket, which was very interesting - RFK opposed the move, but JFK rejected his brother's advice, and acted on his own. Once LBJ was announced as JFK's running mate, the nomination was a formality. After the convention, RFK masterminded the fall campaign for the Election of 1960 (featuring, eventually, the decision to debate Nixon), and the subsequent transition to power.
After the election, JFK started to surround himself with advisers, starting with RFK. While there was evidence that suggests that JFK wanted his brother to be his Chief-of-Staff (after all, he was great at saying "No"), RFK had no interest, in that he didn't want that kind of direct link as an adviser. In the Senate, as well as the media, there was a great amount of resistance to the all-but-certain nomination of RFK as Attorney General, the post that RFK really wanted (as AG, RFK would be JFK's principle adviser on most every question). RFK would have made Cincinnatus proud, in that he didn't actively pursue the post on his behalf, and let his brother, the President-Elect, run point on his nomination. JFK needed to move cautiously when filling his Cabinet, since he didn't receive a mandate from the Election of 1960 . . . he would even nominate two Republicans to his Cabinet (Robert McNamara as SecDef, and McGeorge Bundy as his Nat'l Security Adviser).
(Below: A run-down of JFK's main political advisers, including his brother, RDK as the AG)
Most of JFK's advisers drank the "Kool-Aid" of skullduggery; even JFK believed they could convince nations in the Western Hemisphere that the U.S. was not involved in the attempt to remove Castro from power by force. Arthur Schlesinger (see the above powerpoint) was the only adviser to object to the plan, but he fell in line with the others in order to remain relevant as an adviser - he even stopped a newspaper report about the upcoming invasion. JFK's main motivation for the Bay of Pigs was actually fueled by domestic politics - the political pressure to get rid of Castro in essence forced JFK's hand. One needs to remember that the Appeasement in Munich (1938) was still fresh on everyone's mind, as was the "Loss of China" in 1949, and JFK in no way wanted to be seen in the same light as Neville Chamberlain or Harry Truman. JFK relied on CIA experts, but they didn't provide nearly enough information, as it turned out; JFK would later discover that the CIA actually withheld vital intelligence.
The Bay of Pigs was a disaster: over 120 Cuban nationals were killed, over 1000 nationals were taken prisoner, and four Navy pilots were killed in action in a vain attempt to support the disaster on land. In the end, JFK had no idea how popular and entrenched Castro was in Cuba. The lesson that JFK learned was that he should have known better than to rely on experts without being skeptical; with more information as well as more skepticism, he felt that he would have avoided disaster in Cuba. His advisers learned a lesson as well from the Bay of Pigs: do not contradict the President, even in private, if you want to keep your access and influence intact . . . these two lessons will complicate the U.S. role in South Vietnam for the duration of JFK's time as President.
JFK believed the "Great Man" interpretation of history, in that "Great Men" made decisions that affected history . . . and JFK desperately wanted to be seen as a "Great Man". The Bay of Pigs Invasion reaffirmed his belief that he would never become a "Great Man" if he placed too much trust in his advisers. As a result of the Bay of Pigs, JFK would make greater efforts to parse through the various POVs of his advisers, and then make his own decisions. But others were watching from afar, including Nikita Krushchev of the USSR, and Ngo Dinh Diem of South Vietnam - their perceptions of JFK would lead to far-greater challenges for the youngest-elected President than what resulted from the Bay of Pigs.
(Below: A short documentary on the Bay of Pigs, w/ some insight from JFK's main speech-
writer, Ted Sorensen, a NEBRASKAN)