Considering the vast majority of current Big Picture games use the Xbox360 controller, and that they'll probably already worried about getting enough content working on this device, I highly doubt they will do something so different as a Rift + Wiimote and the like.
My assumption is Rift will be supported, but primary controller will be something extremely 360-like. If not made by Valve than by someone that already makes 3rd party 360 controllers.
The entire idea here is to have a TV-attached device along the lines of the Xbox or Playstation that plays Steam games — so you can sit on the couch with your SO and play some Trine 2 or something. An input device that you strap over your face would make the couch-and-TV integration a bit moot.
That being said it could be a combo, like Rift + a wiimote-style thing?
Mouse + keyboard break Rift immersion, pads are better but still far from perfect.