Judging by the history of VP selections, the main goal is choosing someone who balances the ticket. A candidate is always eager to unite his political party. If he is viewed as a member of one wing of the party, he'll often choose a VP from the other wing. If he "belongs" to a certain region of the country, he'll choose someone from another region. Every presidential candidate has certain salient characteristics, including weaknesses. Often a candidate will choose a VP who provides a contrast. If a candidate is too old, he'll pick someone young. If he lacks experience, he'll pick someone who has a lot of experience. And so on.
It's striking just how often this rule holds true. Consider some recent VP selections and how they were intended to balance the ticket: In 2008, John McCain chose Sarah Palin (young, conservative) and Barack Obama chose Joe Biden (old, experienced, white). In 2004, John Kerry chose John Edwards (young, Southern). In 2000, George W. Bush chose Dick Cheney (experienced). In 1996, Bob Dole chose Jack Kemp (young, conservative). In 1988, George Bush Sr. chose Dan Quayle (young, Midwestern). In 1980, Ronald Reagan chose George Bush Sr. (moderate). Most famously, John F. Kennedy chose Lyndon Johnson in 1960 to help him win votes in the South.
A different method of choosing a VP is to pick someone who reinforces the qualities of the presidential candidate. Instead of balance, this might be called "doubling down." As a general rule, candidates don't do this. Since voters pay most of their attention to the presidential candidate rather than the VP pick, it's difficult for the VP to "add" anything through repetition. A VP's qualities only shine through when set in a contrast. For example, it's unlikely that Obama would have improved his share of the black vote by selecting a black running mate. Nor would a wing of a political party be extra-energized by having both members of the ticket from that wing. If there were a bonus effect, it would certainly be offset by alienating (or failing to energize) the other wing.
For an example of the "double down" approach, one might cite 1992, when Bill Clinton chose Al Gore, who was also young, moderate, and (somewhat) Southern. However, even in that case it's probable Clinton sought to balance the ticket: Gore was one of only 10 Democratic senators who voted in favor of the First Persian Gulf War. Clinton was under fire for being a draft-dodger who had protested the Vietnam War in Moscow; choosing Gore, a hawk, made sense as a balancing maneuver.
Nevertheless, a candidate must be careful not to choose a VP whose qualities undermine the candidate's message. In 2008, McCain's entire argument (almost) was that he was very experienced, and Obama wasn't. McCain then chose Palin, whose main weakness was that she lacked experience. But even in that case, the Republican ticket increased in the polls--until voters discovered just how inexperienced Palin was.
This leads to the final principle, which might be called the "Do No Harm" principle. The idea is that even a good VP probably can't add much to the ticket, but a bad VP can drag a ticket down. There's no question about the damage a VP can do if a VP has major weaknesses (e.g. Palin, whom many voters couldn't imagine being president) or is the subject of a scandal (e.g. Thomas Eagleton, removed from George McGovern's ticket in 1972 after the discovery that he had undergone electroshock therapy and had been diagnosed with "suicidal tendencies").
An aggressive form of the "Do No Harm" philosophy says that a VP can rarely do any good, but can easily do harm, so a candidate should choose the "safest" VP nominee possible--even if it's known he will add nothing to the ticket. This philosophy is questionable. It's difficult to empirically determine whether VPs of the past added nothing to the ticket, since there's no way to test what would have happened if a different VP were chosen. Even measuring poll numbers before and after the VP selection is tricky, because the VP selection usually occurs during or just before the party's convention, which may cause a "bounce" of its own. Instead, one must simply use common sense: Does balancing the ticket enable a candidate to reach a broader array of voters? Yes.
Once we accept that a VP can have a positive impact on a ticket's chance of victory, it's no longer possible to take the view that a candidate should only seek to minimize risk. By its very nature, the value of a VP selection is comparative--it must be weighed in comparison to other potential VP selections. For example, suppose a candidate can choose between two possible VPs. VP #1 would not alter the ticket's poll numbers either way. VP #2 would increase the ticket's poll numbers by five points. Would choosing VP #1 "Do No Harm"? The answer is no, even though the ticket's poll numbers don't go down. It's still a loss of five points that the ticket would have gotten if VP #2 had been chosen. Viewed in that context, VP #1 no longer appears a "safe" choice.
In summary, a candidate should choose the VP who best enables him to maximize the number of voters the ticket can attract. He must balance the ticket, but without undermining the fundamental message of the campaign. He should avoid doing harm to the ticket, while also keeping in mind that it's "harm" to not pick a VP who would add something to the ticket.
