Of course I'm not saying Obama shouldn't pick a VP at all, just that we shouldn't.
Everyone seems to have their favorite for whom Obama should pick for this important position (especially give how much more important and powerful it has become over the last few decades). There are many viable candidates to choose from and many important reasons to choose them. That is why I don't think I can choose the best candidate better than Obama and his staff can.
The office of Vice President is, and always has been, a very important position. Its the #2 position and should anything incapacitate the President they are in charge. This alone make the choice for VP particularly personal to the President himself and has to be a person Obama can trust.
Another major consideration is that the Vice President is in particulary good position for being the next President after Obama's second term (not predicting just stating). So this makes the position very important to the party as a whole. Though there could be different VPs in two terms this has become very unusual looking over the last century. This factor alone is a huge consideration when screening the candidates.
Though originally the VP was not really a position that wielded any true power, over the last few decades this has become less and less true. In many ways the VP needs to be as skilled a politicion as the president. (though its hard not to think these days the VP is doing both jobs lol) We all want a competent VP, one that can help OBama with the overwhelming number of tasks that lay before him.
Lastly the VP is almost always someone who help pick up a state, region or demographic (or mix of these) for the ticket. Talk about complicated? Polls have to be run on every posible combination and often in regions that aren't helped to see if they hurt.
On top of all this the candidate has to be vetted for dirt and skeletons. This takes many rescources and high level access to do with any real compitence. We know the Republicans are going to look for dirt so the Dems better know about it first to have a defense or disqualify the candidate.
So there looks to me like there are 5 major aspects to picking the VP. There are some I feel like I can make a pretty informed decision. I have some ideas on who would have the skills and capabilities to be the VP and maybe the next president. But, I don't know who Obama feels comfortable with and I don't have the polling data to see who helps and hurts. I definately don't have the resources to do thorough background checks.
In short, I don't have the ability to pick a better choice for VP than Obama and his staff can, so I'll just let them do it...