The Arlanda Express is fast and convenient. If you're traveling with someone else or your travel bridges a weekend, you can qualify for a nice discount. Otherwise the bus (Flygbussarna) is a good alternative.

The Stockholm Card can be a good value if you plan well and cover a lot of sights during its period of validity.

Don't miss the Vasa Museum. The Royal Armoury is pretty interesting as well.

An AMS layover of 55-minutes is do-able, but I'm with heatz: I'd try to make the outbound connection state-side. On the way back, you may consider engineering an overnight layover at AMS for almost no added cost, if you are interested in spending a little time in Amsterdam. On the DL flights, try to book an exit row seat (at no extra charge); your companion can sit with you in the exit row if he or she is physically qualified to do so.