I believe the vice-presidential pick needs to fill a few roles.
*Energize and/or expand the base
*Serve as an adviser
*Have name recognition/credibility
*Be an effective President of the U.S. Senate
I notice suggestions for conspiracy theorists, anti-war liberals, economists, and tv hosts in this thread. I think it would be a better idea to pick someone from the current crop of Presidential candidates. One because their name is out there and people know about them, and two we should leave what good people we have in Congress.
The vice president doesn't have to be a mirror image of the President. George H.W. Bush was much more moderate than Ronald Reagan but he helped him get elected. On the other hand, Palin was the reason McCain didn't get beaten even worse. I believe the base needs to be firmly secured and that means making sure all Republicans come out to vote. (Not all are comfortable with Paul, or his age for that matter).
Of the current field, Newt and Santorum are definitely not possibilities. (Newt would be good in a cabinet role though). I predict Bachmann will get destroyed by the media just as Palin was, so while she could fire up the base she is poison. Even though Romney and Huntsman are moderates, they would bring a good deal of credibility and experience. Furthermore, both are excellent fundraisers and have an abundance of personal wealth. They would be options if we wanted to go the George H.W. Bush route. But would the sharp difference in philosophy be a problem? Gary Johnson is the most similar to Paul as they are both libertarians, but has a huge lack of charisma. Herman Cain would be a good choice. He consistently registers the highest positive intensity scores so he could fire up the base; he has a strong business background, is a social conservative, and would dismiss the race card. Tim Pawlenty would be a very solid choice and people can generally trust him, yet like Johnson he has a serious lack of charisma.
I am partial to Cain, but I think he is the best choice.