Raspberry Pi that runs the python program that sends video to the webserver using ffmpeg. Adafruit Motor HAT to connect the motors to the pi. Android phone is strapped to robot that runs a custom android app that receives chats from the website and also says them out loud using the Android API for text-to-speech. Everything sits on top of a 3d printed chassis. Cheap logitech webcam. Web app is a node server, socketio, ec2.
The main parts are a RaspberryPi, some Adafruit stuff, and a motor from pololu. Also, I put all the parts in a package that you can get here:
http://runmyrobot.com/kit
This is exactly what I have been looking for, reasonable hardware that I can put together with a drivable car/robot that I can have fun programming. I will watch your video and probably order your kit. I think my son could really enjoy learning with this kit.