Ideally she’d want a non-white male from a swing state. The Republicans are unlikely to try to hit Hillary on inexperience (especially if they run Trump) so she’s probably going to either want someone who seems young and fresh and non-white, or maybe go with a Safe White Male.
Unfortunately, the Democratic bench is actually rather thin these days. Not a lot of Blue governors outside of places like California (and she’s not going to pick Moonbeam, even if he wanted the job).
Julian Castro and Tim Kaine seem like reasonable picks.