My note:
Cheapest by far is public transport, SL, a 24 hr card is 115 SEK. Plus 20Sek card price. The bus 583 to Märsta runs fairly often, every 15 minutes during the day, takes 15-20 mins or so depending on which terminal, trains from Märsta runs every 15 mins, approx travelling time to Stockholm C is 35 mins. The total time one hour. Tickets can be purchased in Terminal 5 (information desks, Pres*****yrån or 7-Eleven [newsagents]),
The travel card also valid for travel on the Djurgården ferries between Slussen and Djurgården (operated by Waxholmbolaget).
the number 69 bus or number 7 tram is a superb way to discover Stockholm. The lines go out to Djurgården and major attractions like Skansen(too far) and the Vasa Museum.