- Probably the single most important thing. It's very rare to work at a school higher than the one you graduated from.
- Doesn't matter a whole lot. What you did there is generally the most important thing. Research, teaching, publications, grades, test scores really matter the most. You want to go to the best school you can, but if you end up at a well known private school or big state school/flagship, you can go anywhere. A commuter campus, maybe not.