Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
I am new to the world of embroidery but we just did a couple hundred left chest on the bottom of the barrel moisture management shirts and used two layers of medium cutaway and that worked well for us.I know this is not very specific so it might not help much but I thought I would offer what little information I had that was related to your question.
Performance backing is a way to go. Cutaway looks Ok when embroidered, but curls up over time.I'm working on some Nike moisture wicking shirts to and use performance backing only. On really thin ones, I will use black mesh in between the backing and the shirt to prevent white showing through (Dark shirts).This is my first time using performance backing, but right now, it looks much better than anything else I have used before.