If the church directly pays the tuition of a staff member to attend classes or pursue a degree in order to better serve the church, what part of that tuition should be included in the employee's compensation on a W-2?

Depends on how much the tuition is.

Reimbursement for tuition can be tax-free if it is below $5,250.

So if the tuition paid is $5,250 or less, no taxes need be paid.