There are at least three ways to think about Veepstakes.
One is in terms of immediate electoral effect. I've written quite a bit about that...the short version is to avoid disaster by picking someone as vetted as possible, and then look for the upside of a couple points or so in the running mate's home state.
The second is in terms of defining the party. In part this is because the Veepstakes winner is apt to become more important within the party, perhaps even president. Or we can look at it the other way around: Veepstakes isn't just a free choice of the nominee, but one that is affected by preferences of party actors. That's what we're seeing happening this week: party actors are mobilized by the selection, and make clear to the nominee their preferences and especially their veto points. And, in turn, nominees -- who are in an excellent position to understand the strength within the party of various people and groups, having just navigated all of that to get nominated in the first place -- have to judge what is a serious problem for party actors who really matter, as opposed to mere posturing or, perhaps, strong feelings of those who can be ignored.
Then there's a third way. We can think about who is best equipped to do the actual job of a vice president.
The problem with that one is that presidents are not only free to match the VP's tasks to their particular talents and skills, but they also are perfectly free to enlarge or shrink the VP's responsibilities. And from the point of view of the president it's not entirely clear that the president is better off with a Gore or Mondale rather than a Quayle. Let alone a Cheney. There's a problem with the vice president, which is that they more or less can't be fired.
Anyway, if you do want someone to help with governing, I'd argue it's better to go with someone good on process than someone with substantive expertise. And the two Veepstakes rumored candidates who seem to have the right experience for that are Rob Portman and Bobby Jindal. Portman has served in both chambers of Congress and in two presidential branch agencies as US Trade Rep and OMB director; the latter is certainly a good perch for knowing a lot about executive branch politics. Jindal also was in the House, and his experience in state government seems useful; he was also at HHS, so he knows a bit about executive branch agencies, too. Since Mitt Romney is a former governor, that would seem to suggest that Portman's experience is a better fit. In particular, note that each the last three presidents have had a Chief of Staff who had previously been OMB director (Lew, Bolten, Panetta). On the other hand, Portman was only at OMB for thirteen months, and I should note that I'm only talking here about what positions they've held; I have no particular knowledge about how well they did there.
I have no idea what Romney will do, but it sure seems to me that of the people who are getting lots of mentions, Portman is a very logical choice.