Both the trains and Flygbussarna are very convenient. Public transportation is not a good idea- you would have to take a bus to "Marsta" and then switch to a train at least once, if you have luggage I don't think this is a viable option. But if you are 3 adults I would suggest taking a taxi to the Sheraton usually 450SEK which is obviously less than the bus and perhaps twenty minutes longer than the express train but it would make up for time considering the walk to the Sheraton.