Scoop Jackson, HHH, and Orville Freeman were considered as well.
LBJ, while on shaky terms with the Kennedys, was, I think, JFK's best bet.
We can debate the merits of the vice presidential picks, but I will argue it is a bit of obsfustufucation on the issue of winning the 1960 election. Kennedy/Johnson held a rather strong lead due to serious missteps by Nixon. It was relatively later in the campaign that Nixon came from behind, hence why it was as close as it was on Election Day. So I would argue that Kennedy can win with another running mate depending on the shape of the campaigns. However, Johnson was the best choice because he was so strong of a running mate and pushed Kennedy over the top following Nixon's recovery.