Leadership selection will likely always be at least somewhat idiosyncratic, and there can be little doubt that those doing the selection are trying their best to select the very best leaders.
Still, there is some data arguing that these factors receive weight (or act as a filter) in the leadership selection process.
“Highest tithe payers”
Leonard Arrington noted in his diary, dated Aug 17, 1992, his frustration with the practice of the day (from this article):
Appointing the highest tithe payers to positions of leadership rather than the most capable or worthy. In choosing stake leaders, the General Authority comes with a list of the 15 or 20 highest tithe payers and starts down the list to choose a stake president and high council.
Relationship to current leadership
One’s relationship with an existing general authority may influence higher leadership callings.