I'm expecting a 'Wii2' to be mentioned at E3 - I say 'Wii2' as I'm expecting an iteration of the existing technology rather than a revolution. It will most likely have a screen on the controller however I doubt it will be HD and I doubt it will be up to much beyond acting as say a PDA style device for use in-game. Anything too large will detract from the controller.
As for the controller, I'd possibly expect to be able to use existing MotionPlus Wiimotes and a new controller - why? So they can keep the core 'Wii' play scheme which makes it what it is, alongside the new controller to allow for a much better chance of 360/PS3 ports to work well on the Wii.
Performance wise I'd be surprised if it isn't 1080p, the same optical drive as we have now, quite possibly a multi-core variant of the GameCube/Wii CPU with a much more hefty GPU chucked in. It doesn't need massive amounts of RAM, it's a console and not a PC, though it will likely have more than the Wii does.
Last but not least, a camera on the sensor bar is pretty feasible, cheap enough to add vs. some of the other wierd and wonderful rumours.
Size? I'd love to see it comparable with the size of the Wii, though I suspect it may be a touch larger.
Launch price of �£229.99 with a MotionPlus Wiimote and a 'new' controller, bundled with something like WiiPlay-HD. In black only at first...