Visa on arrival at a cost of USD30 now applies for many Europeans. I don't whether that applies to Swedish nationals or not - do check. I've not been to JKT since this has been in effect so I have no idea how it has affected immigration processing. However, I can remember seeing a seperate visa booth at Soekarno Hatta so the new process shouldn't have slowed down the actual immigration processing that much.
The best bet for a taxi in to town is to turn left once out of customs and head out to the curbside. You need to find the Silverbird taxi rank - you'll recognise the cars as they are similar to the taxis used in SIN and HKG, only painted black. Can't remember the fare but it shouldn't be more than USD10. Getting a Silverbird back to the airport might be a bit more tricky as they don't cruise around that much. The nearest 5 star hotel or shopping mall should have a rank though. Time can be anywhere from 30mins to 60 in my experience, depending on time, weather, alignment of Venus and where you are going!
To reduce the hassle factor, why not pencil in an overnight stay - the Shanrgi-La, Grand Hyatt and Mandarain are all central and good hotels. Or try the Dharmawangsa for a design hotel experience.
We have a couple of JKT residents on the board and I am sure they will be able to chip in with more adivce.