I've completed my ARN portion of the trip and just wanted to add some note to make this thread complete and more useful to future searchers:
STOCKHOLM C is attached to the T-CENTRAL T-bana station. The #36 train platform is about at least a brisk 5-7 walk.
The frequency of the #36 train is about once every 20 minutes (confirm when you go!) and the ride takes ~45 minutes from STOCKHOLM C to Märsta. The #583 bus frequency is ~every 15 minutes. The bus ride takes 10-15 minutes to the airport.
At the airport, you can buy the ticket from the many tourist INFO offices. I think there are automated machines as well. The INFO offices take credit card.
Alternatively, if you don't need a public transit ticket, or are in a hurry, the train (Arlanda Express) takes only 20 minutes. There are several bus services that cost ~$100sek. Some are as low as $85sek.