I assume you want to impress your significant other, so let me suggest you fly UA 382 - ORD-IAD aboard the 747-400

That's style and those are business class seats. No one forgets the experience.
Regarding GRU there seems to be a company that keeps your luggage per GRU website. It's in Portuguese so the direct link is
http://www.infraero.gov.br/www/NHome...uarda%volumes# and it shows it immediately after you leaving Customs.
There are airport buses that in 40-60 min take you to the city airport, downtown, Financial Area (Jardins) and the Bus terminals. I'd rely on these buses to get in/out of the airport and to take you to the Bus Station in the evening. Safe, reliable and inexpensive (7 USD/person).
Enjoy Sao Paulo !