Does the space station orbit or is geostationary?

It orbits the Earth.

However, even communications satellites in geosynchronous orbits are in orbit around the Earth; it's just that each orbit takes exactly one day, and so the satellite appears to be stationary above a point on the Earth. We can use this fact to our advantage; instead of building tracking antennas that follow a rapidly moving object, a tracking antenna for a geosynchronous satellite never needs to be turned.

Which is a good thing, because those little "Dish" and DirecTV antennas can't be easily turned!