Since he has already decided that a woman will be the Vice-President that hardly delimits choice. The list of people with extensive experience in governance and executive decision-making will make the choice that much more difficult---there are so many who could or should be President tomorrow. This shifts the matter from who to choose----an impossible task for the good fortune that comes with having these choices---to _how_ to choose.
Putting on my political pundit topee I think there are two strategies.
The first would be more traditionalist insofar as it is a calculation that weighs votes. Do you choose the person who might help you carry a State? Has this in fact happened since, say, LBJ? A region? So a midwesterner? To keep the Senate and not turn it over by "risking" a Blue Senator? This would be the only political calculation I would recommend. Biden is going to need every single vote he can get if McConnell retains his seat and Joe needs 60 votes.
But the wiser strategy is to invite someone who not only has all the requisite gifts and experiences but one who will push back, one willing to be an alternative, a contrarian. If you are looking for someone who will think _with_ you and be _for_ you then you need someone who has the courage, the emotional maturity, and the intellectual audacity to come at you. You need someone who understands how to make an argument and reach into worlds of ideas and experiences that are _not yours_.
Everything about Trump is a nightmare but one of the worst features of his malignant narcissism is that he has no capacity to feel for others, sympathy, or to attempt to feel as others, empathy. Empathy is the most complex experience we can imagine because it is the unreachable state.
We really never have another's experience; that is not possible. But we must try, we must imagine, we must do all we can to rally the resources of feeling and thought to attempt to feel as another. This is audacious and it is humbling. It requires that paradox: to say "I feel you" _and_ to admit "I cannot say I know how that feels." Both are imperatives of empathy.
This paradox is another reason Biden needs someone capable of pushing back, questioning, cajoling, and maneuvering to see other points of view. I think if this is the focus then Joe will choose Kamala Harris. She was the one who forcefully declared first her emotional hurt and her disagreements with Biden over the past. Senator Warren offers many of the same markers.
So this pundit says it will be one of these great women and I would bet on Senator Harris. She has all he needs to make sure governance, competence, compassion, and seriousness are once again American ideals.