Hi! Here are a few links which may be useful if you want to get started building self-balancing robots! I found that with the components below it's easy to achieve some nice results very quickly (<5h)!
I used the Arduino 101 to control the robot. It's quite amazing because you get the 6-axis accelerometer and gyro directly on the board. Everything you need to use the sensors in your code is very well-documented here.
Now all which is left are two motors, a motor shield, a battery, wheels and a frame. You could use the da Vinci Mini 3D printer to build the frame.
Here's a video and a few pictures:
Many thanks to A. Holtkämper for designing and printing the frame!
Let me know what you think or if you have any questions!