In all the pictures you see of the Supreme Court where they're posing for a picture (i.e. - not on the bench), they're just sitting in simple Windsor chairs. No big fancy plush red leather chair. Just simple wooden things.
I looked at a few older pictures as well and that seems to be the approach for quite a while.
Interesting Supreme Court connection: Justice Rehnquist lived about a quarter mile from my parents' house in Arlington. My sister played on his grand-daughter's basketball team back when she was in middle school, and we would see him at games every once in a while.