I go to Stockholm a lot.
The Arlanda Express is good, just follow the signs. The airport bus runs regularly too, terminating its journey at the central bus station. It's cheaper and reasonably quick.
There are now lots of 'boutique' hotels in Stockholm, some of which are quite quirky and fun. There are also some basic but cheap B&B type hotels, often in converted office blocks. Prices? Well booze is more expensive than the UK but, at the current rates of exchange, not much more than you'd pay in London.
Buy a tourist travel card for the (very good) underground and bus system; you'll probably find that your mobile works on the underground, too.
The 'Old town' - Gamla Stan - is popular enough but the previously run down areas of the city are where all the kickin' night clubs are.
If you want to go and buy some Rukka, Joffarma or whatever gear at prices that will near enough match FC Moto, go to:
http://www.mcvaruhuset.se
at NORRA STATIONSGATAN 93. You can walk in about 30 minutes from the central station or take the underground out for a couple of stops and walk about 10 minutes. If nothing else they all speak English, you'll get a coffee and you can look at their virgin RC30 and NR750.
PS Pick up a free street map at any hotel or the tourist desk at the airport. Everyone is very helpful.
PPS If it's on, maybe watch some ice hockey at the Globe arena or one of the local stadiums. Even if you don't follow all or any of the rules, it's worth it for all the razzmatazz.