Since I just came back from ARN, some more notes/details :-).
Take the shuttle bus - they have power (230V Europe outlets) +free Wifi!
http://www.flygbussarna.se/en/arlanda
You can buy tickets online, at a vending machine (VISA+PIN) or at the 7eleven (215 SEK return).
Note that you will spend some 45-50 minutes per leg (they depart every 10min over the day) - but they've fastlanes (Taxi not..).
Have fun in Stockholm, it's a very nice city!