Beginner topic - type of wire for motion projects?

I don't know if this will help but sometimes having a name to go on can set you down the road. A fairly supple and abrasion resistant wire insulation is called TXL or if you want thicker GXL (TXL ~= Thin cross linked polyolefin) GXL is something similar just thicker. TXL is used in the automotive industry for wiring harnesses. You can specify the number of strands as well. Good luck.