What is the relationship between Teagueduino to Arduino?
The teagueduio seems to be both a hardware and software wrapper to an Arduino Nano or compatible board. Basically it shields you from reality (i.e. the microcontroller and low level programming) even more than the Arduino platform making it even easier to use and less adaptable. You will be able to accomplish fun little projects with little effort or knowledge. This will maximize your fun at the cost of its longevity and deep learning. Whether it is right for you or not depends on your objective. If you know nothing about electronics and programming it is a great place to start. But, if you want to become really proficient at electronics this is just hiding most of the details. I don't support jumping over the fundamentals of a topic just to get to the fun parts. Therefore, I would recommend one of those X-in-1 (where x=100,200,...) electronics type trainers before this personally. A book with a few components and a bread board is great too. 

The migrating to Arduino looks as simple as physically unplugging the arduino board from the teaguedunio board and using the arduino IDE instead of the teagueduino's.