Is this to be used in a moving vehicle/vessel, or just static? For static use you just need a dual axis accelerometer - or a plumb line. To solve it in a moving system is much harder and you probably want to start by looking at home the autonomous drones do it - they often use Arduino clones with the required sensors integrated, and their hardware and software might be a good starting point for your project.
Project is very well doable, but it depends on your experience with programming and electronics. Depending where you got the sensors and the TV out shield you can probably download sample code that will do 90% of your goal. Only step is probably to integrate these and add your "visual art" over it.If there are problems let us know..
The way autonomous drones do it is by sending data over the air and then processing it on a computer.