"Ted Kennedy campaign announcement of people he is considering for his running mate stated. Reubin Askew, Tom Bradley, Lindy Boggs, Shirley Hufstedler, Henry Jackson, Richardson Preyer, and Adlai Stevenson III listed."
https://tvnews.vanderbilt.edu/programs/512390
My guess is that he goes with a southerner like Askew. The mention of Boggs [1] and Hufstedler and Bradley was probably just to show that he was "considering" women and African Americans. Jackson was just too hawkish.
As for which running mate would enable him to defeat Reagan, my answer is, None of them. The Democrats would just be too divided. A lot of Carter voters would not vote for Kennedy in Novmeber (just as in OTL many Kennedy voters would not vote for Carter). Also, when a president is unpopular, voters tend to take it out on his party, regardless of its candidate.
[1] Of course she was also a southerner--but (among other objections) I'm not sure if the country was ready for a ticket of two Catholics...