There are different strategies that presidential nominees pursue when selecting their running mates. One of the most popular is creating regional balance. For example, John F. Kennedy needed to reassure the racists in the Democratic Party, so he picked a Texan. That Texan became president when JFK was killed in Texas, and he compensated by picking a pro-civil rights northerner, Hubert H, Humphrey, That Texan also became the greatest champion of black rights since Abraham Lincoln. Jimmy Carter followed that model by picking Minnesota Senator Walter Mondale as his running mate.
Another strategy is to pick someone to excite the base of your party. Nixon did this with Agnew. McCain did this with Palin. But something related is trying a desperation move by appealing to some racial, religious, ethnic, or gender group. Mondale and McCain did this with their picks of Geraldine Ferraro and Palin, respectively. Gore did it with Joe Lieberman.
Another option is picking your strongest rival. Reagan chose this path. It shores up divisions in the party. Obama made his chief rival his Secretary of State, which is not much different in its intention.
Another option is to pick someone who is an ideological fellow-traveler. I think Dole had this in mind when he selected Jack Kemp. I think Clinton did the same with Gore and Gore did the same with Lieberman.
Another strategy is to pick someone who makes you look good by comparison. Nixon did this with Agnew. Poppy Bush did it with Dan Quayle.
Finally, you can pick someone strictly for what you view as competence. I think George W. Bush did this with Cheney and Obama did it with Biden.
As you can see, there can be some overlap. But assuming Mitt Romney pulls this thing out and wins the nomination, how do we see him going with his vice-presidential pick?
He could go for regional balance and look for a southerner. He could pick someone who makes him look awesome by comparison. He could pick an ideological soul-mate, although no one seems to know where he really stands on the issues. He could pick his strongest rival. He could make a desperation move to try to win latino votes or the support of women. Or he could go for someone who he truly thinks is up to the job.
Feel free to use the same criteria to guess who Santorum or Gingrich would pick.