It’s a bit too soon, even in the aftermath of his New Hampshire victory, for Mitt Romney to start picking a running mate. But it’s not too early for us to have some fun thinking about it.

The veepstakes is one of the great political parlor games, an exercise both fascinating and overrated. A bad pick can hurt a campaign, as John McCain learned last time, but only in the rarest of instances does a No. 2 help a presidential candidate win the White House.

(Could Hillary Clinton be an exception? Former New York Times editor Bill Keller is sure promoting the idea. But that remains a fantasy, given the remote likelihood that Barack Obama would dump Joe Biden.)

If Romney is indeed the GOP nominee, he faces the most important decision of his campaign—not because a running mate will drag him across the finish line, but because the country will judge the way he makes his first presidential-level decision. Traditionally, there are three major factors to consider, although these may be relics of the past.

In the old days, geographic balance was practically a must. But ever since Bill Clinton of Arkansas picked Al Gore of neighboring Tennessee, that seems less important in the media age.

A second consideration is selecting someone who can deliver a crucial state. That may well have worked in the 1960 election, when Lyndon Johnson helped Jack Kennedy carry Texas. But Lloyd Bentsen couldn’t do the same for Michael Dukakis, and John Kerry lost North Carolina even with John Edwards on the ticket. The last two Republican nominees abandoned the key-state approach: Dick Cheney’s Wyoming and Sarah Palin’s Alaska don’t count for much in the Electoral College.

The final measure, ideological balance, may still resonate. With Bush-Cheney, McCain-Palin, and Gore-Lieberman, for instance, the winning candidate was trying to make inroads with the other wing of his party.

But an underappreciated virtue, in my view, is stylistic balance. Biden’s voluble, back-slapping liberalism provided a counterpoint to Obama’s cool, professorial air; George H.W. Bush gave Ronald Reagan entree to the Republican country-club set; the patrician Kerry needed the populist Edwards; even Palin initially brought youth and excitement to the aging warrior McCain.

But the Palin pick, like that of Dan Quayle, underscored a more urgent reality: you have to choose a plausible president, someone who is viewed as being able to take over at a moment’s notice. And Romney, the M.B.A., will surely include that on the balance sheet.

So how do some of his potential running mates stack up?

Chris Christie. The rookie New Jersey governor, who many thought could have grabbed the top prize had he jumped in the race, has been campaigning hard for Romney. He would bring passion and blunt talk to a nominee who often sounds like a coldblooded management consultant. And while Christie himself loudly proclaimed he was not ready for the presidency, many voters might conclude he passes the plausibility threshold.

The downside: Christie doesn’t have the personality of a No. 2. As the kind of Northeastern moderate that Romney was once proud to be, he may not have a record that reassures conservative voters already suspicious of Mitt. And his big mouth would undoubtedly get Romney into trouble. (The other day, after some women at an event started chanting about jobs going down, he said, “You know, something may go down tonight, but it ain’t going to be jobs, sweetheart.”)

Marco Rubio. Every discussion of veepdom seems to start with the freshman senator who might be able to pull the crucial state of Florida into the GOP column. He’s young, dynamic, and, in case you hadn’t noticed, Hispanic. The historic nature of his candidacy would undoubtedly energize the ticket.

The downside: Rubio, as he’s told me and lots of other people, doesn’t want to do it. Perhaps he senses that questions will be raised about a vice-presidential nominee who will have been a senator for a year and a half. And the Cuban-American may get mixed reviews in the Latino community, where some view him as a turncoat for his hardline stance on illegal immigration—a position that is also a problem for Romney.

Nikki Haley. The South Carolina governor, who also has been hitting the trail for Romney, is a polished performer. She is a favorite among true-blue conservatives who could serve as an ambassador to the right. She would become the first Indian-American on a national ticket. And by running with a woman, Romney could broaden his appeal to female voters who might view him as having all the warmth of a district manager bearing pink slips.

The downside: Haley, too, is inexperienced, a former state lawmaker serving only her second year as governor. Obama is not going to carry South Carolina no matter who’s on the ticket. And in the heat of a campaign, would that blogger’s allegations about having an affair with Haley be resurrected?

Rick Santorum. The former Pennsylvania senator could help spark enthusiasm among social conservatives wary of a nominee who once favored abortion rights. As the grandson of a coal miner, he has a certain blue-collar appeal that the son of the former head of American Motors clearly lacks. Santorum also brings 18 years of Washington experience, which would be useful in navigating the treacherous Beltway waters. And Romney would help unify the party by reaching out to one of his campaign rivals.

The downside: Santorum is a long-winded campaigner who gets tangled in talk of subcommittees and amendments. He may have limited appeal to independents, judging by his 18-point reelection loss in 2006. And tapping Santorum would put the spotlight on his more controversial positions, such as that states should have the right to ban contraception.

Kelly Ayotte. The freshman New Hampshire senator, who provided a key endorsement, is a Tea Party favorite who would rouse the conservative base. Ayotte is a former state attorney general with hardline foreign-policy views. And New Hampshire, while small, is definitely a swing state. “Expect to see her on a presidential ticket one day,” writes Washington Post blogger Jennifer Rubin.

The downside: Few people in America know who Kelly Ayotte is. That not only produces a stature gap, it means a roll of the dice because she’s never been vetted by the national press corps. One school of thought is that no candidate should pick an obscure running mate because the press will have a field day digging up embarrassing anecdotes and scandalous material.

David Petraeus. As a widely admired ex–military man, the retired general would bring instant foreign-policy cred to a candidate with no experience in that realm. Petraeus is a master at charming reporters and would be an out-of-the-box choice.

The downside: His presence on the ticket would put Iraq and Afghanistan on the front burner at a time when Romney wants a laser focus on the economy. Petraeus has never run for office and would make mistakes. And he has a Jon Huntsman problem, having given up the uniform to serve as Obama’s CIA director.

Sarah Palin. The upside: She’s been there, done that.

The downside: See above.