Every time Nintendo introduces a new thing into controllers, we should expect a version of it on new platforms if only for Virtual Console reasons. There absolutely will be a Gamepad successor. Whether it's included with the console remains to be seen. Personally, I doubt it. I think most first party games will have a GamePad enhanced control option, and games that require it (e.g. Splatoon) will have a version sold with it. Otherwise, it will be sold separately in stores, and there's reason to believe that Nintendo will allow the 3DS successor to function as a GamePad. Nintendo pushed the GamePad as a luxury item when it clearly wasn't. The most expensive component was a six inch 480p screen which was low-end even in 2012.
I think a traditional controller will likely be the pack-in controller if only for simplicity's sake. Most Wii U games had a Pro Controller option while few required the GamePad or Wii Remote even if they were arguably better with the latter options. For those that want to play Wii games on Virtual Console, they'll have to buy a motion control remote separately. I'm curious how Nintendo is going to handle that. I have doubts it will include the port for the sensor bar. Maybe Nintendo releases a USB sensor bar, or just ditches IR-technology altogether because it's awful. If Skyward Sword did anything right, it showed that the gyroscope in MotionPlus did a better job simulating pointer controls than the regular Wii Remote did with actual pointer controls. Nintendo likes 1:1 emulation, but I hope it reconsiders since the gyroscope worked so much better.