I use wire wrapping wire (16 awg from memory) for everything internal. Its very thin, handles about 1amp, single core so no stray strands, but flexible at the same time. And it holds it's shape so you can Pre bend it before you solder.
Highly recommended!
For things that leave the casing I would use a multi strand copper wire to withstand flexing, gauge isn't that relevant for most of what we do, video games don't draw that much current.