Oversimplified, I'd say the same guidelines that should be applied to all leaders - past performance, vision for the future, loyalty, in this case, to the Church, clean record, a proven ability to lead. Leadership candidates have their champions, and their detractors, so perhaps there is a little politics thrown in.
As you know, The Cardinals elect him. It is said that the chosen one does not have to be a Cardinal, or even a Bishop - a parish priest is eligible.
Have you read, "The Shoes of the Fisherman"?
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