Zot - we will be on the Grand 8/17, when are you going?
The cost for a cab from the airport to city center in Copenhagen is about $25. We are going 3 days early so we will buy the Copenhagen Plus Card. It includes the train from the airport to the city so we will take that. They can accomodate your luggage and pick up is right outside the international terminal at the airport. We'll then take a cab from the train station to our hotel - the Phoenix. Many hotels are located very close the train station/Tivoli area. Also, cabs in Copenhagen are set up to accept credit cards.
I'd be glad to share the information I have "collected" about Copenhagen. If you want me to send it to you, just email me. email@example.com