How easy/cheap is it to get a small apartment...?
No startup scene, but a 1,300 sq. ft. apartment in the center of town (3bd, 1.5 ba) goes for only $1,500/month, and the commuter train to Gothenburg takes about 45 minutes.
If you have money you can get a "business apartment" for about 2x the normal rate. Those are pretty easy to find. But you'll need to have a business first (even one in the US) to rent it.
You can get an idea of what's available using the aggregator http://kvalster.se/Stockholm . When a place is "1 rum" it means studio, "2 rum" means "living room and bedroom", etc. As a decent approximation, 1sq meter is 10 sq. feet.
Rates in the tech area of Kista look about $700 for a shared room/studio. In Södermalm I see prices more around $800 for a room/studio, though you can pay a lot more. (350 sq. ft studio apartment, furnished, for one month rental while the owner is overseas, $1264 for the month.)
It is possible to get a sublet or such but it tends to be expensive and quite time consuming. A lot of scams going around as well so one has to be careful. Prices indicated above seem quite accurate.
But when I first moved to Gbg it was easy to get a 2nd-hand contract. Now it's nearly impossible. I read that there was a change ~5 years ago in the law to make it financially better for the Bfr to switch from rental to co-op, so I can see how that would also affect Stockholm.
Well, if I want my children to retire in Vasastan then I should put their name on the list soon. (And have children, but that ruins the joke.)
Some current listings from the Swedish equivalent of Craigslist:
If you don't mind (or prefer) living in the suburbs you can definitely reduce your costs a lot.