2km/s means you are limited to about 20% payload. 20% is 10x better than a normal rocket, but there are actually easier ways to get 20%.

The beamed power method gets about 20%, and works for humans (no g load). Escape Dynamics is trying it: http://escapedynamics.com/edispacelaunch/.

The difficulty here is more technical/scientific than engineering. Synchronizing microwave beams is hard, and if you don't you get destructive interference. I don't know if they have solved that problem yet (there have been a few proposed solutions, we'll see if any work).

Edit: Yes, rail would work great on the moon/mars. Actually there was a movie (Moon, with Sam Rockwell) where fuel is harvested on the moon and shot into orbit. Fun, crazy movie.