The Arlanda Express is definitely the way to go, especially as you will be getting in at 7am. I took the bus once, as in normal season it is quite a bit less than the train, and we got stuck in traffic inbound to city central.

That was the last thing we wanted after flying allnight. The train has 2 stops at the airport,and then direct to city central. Perfect for your hotel.

If you don't have it yet, here is a link:

http://www.arlandaexpress.com/

Just click on the english link on the top of the page.

If you have time,take in the changing of the guard at the castle, about a 10min walk from your hotel. Have fun