I have looked into this a bit and though I don't have a lot of experience in the field I have spoken to people who do. The general consensus is that to become a game designer you should start out as a level designer. Basically because you have to work with writers, manage assets, write scripts, and A LOT of naming conventions. At least thats what I'm told by reps at both Ubisoft Montreal and Rockstar Toronto.
With that in mind I highly suggest that people who want to get into game design should take level design as a logical first step.