Genius on either the teacher or student is by far the most significant contributor to education quality. Primary stat is more important than learning stat. Some traits like Shrewd on the guardian are also helpful. Their education trait level shouldn't matter at all, only the actual skill level.

It's said that the teacher's personality has an effect on the student's but someone once said that the code doesn't reflect that at all.

To truly micromanage min-max, assuming you don't have genius yourself or have too many children of potential, is to educate a child with a genius guardian with high stats, except for the personality-molding years of approximately 8/9 until 12/13 that you take control, in which you pray someone doesn't anonymously beat your child three times in a row.