From Airport to Copenhagen Marriot - Kalvebod Brygge 5

The Marriot is a few blocks from the central station, so you can take the regular train from the Airport to Copenhagen central. Plan allpublic transport in Denmark with www.rejseplanen.dk

You don't really need a shuttle company to get from your hotel to your cruise ship...just dial 35 35 35 35 for a taxi. I'm sure the concierge at the Marriott will help you with this if you don't want to use your phone.
Getting to central Copenhagen from the airport is very easy. Just get onto the S train (both lines go to Kobenhavn H; central station). The S train can be caught right inside the airport and it's about a 15 - 20 min. ride. Once you get to Kobenhavn H, go out the main doors that face Tivoli Gardens (right across the street from the station) and turn right. It's about a 10 minute walk to your hotel. There are also taxis right at the station if you'd rather not walk.

Take the train, it is easy with luggage. Also, taxis are very expensive in Copenhagen.

The original post is from June and judging from the OP's other posts it was for a trip this summer, so the information is irrelevant to the OP (who never bothered to answer any of the posts btw).
However since this post has resurfaced again, I just need to clarify a tiny mistake in Anitas reply. The S train (Copenhagens suburban commuter train) does not run to the Airport. I know that this is nitpicking (sorry Anita :-) ) and it is of little relevance if you need to get from the Airport to Copenhagen Central, since there is only one platform at the Airport station. However if you need to get from Copenhagen back to the Airport, you would end up on the wrong platform if you tried to take the S train.
Øresundstog trains, Regional and some intercity trains connect Copenhagen Central and the airport.