Not to make fun of this post as I just got my GC two months ago. I will go
back China visit my family in the summer. So this question actually applies
to me as well.
AFAIK, passport and green card should be enough. If you have old passport,
you may want to carry it with you as well.
A US driver license might be useful. 身份证。One bank card, one credit card.
Health insurance card.