Starching the fabric will help for sure...depending upon the font and design, if you still get puckering use an iron on backing like Cloud on the fabric first, then embroider your label using a tear away stabilizer. The Cloud backing will give the fabric some body and it will not show through the fabric...I find this helps quite a bit...it will also stabilize the fabric and prevent any stretch of the fabric that could also cause puckering.
I would starch the fabric. I digitise my own labels using a font that is quite a lot less dense than most. (I think puckering is often due to using a design which is too heavy for the fabric.) I use tear away stabiliser.
I wish I could help. I know one thing that starching the cotton will help. Do you have enough material to do a test piece? Hopefully others come with advise.
Thank you. Yes, I have plenty. I was planning on starching. Not sure if I should use a cutaway or something that will stay with it for stabilizer. I'd like to try plenty of starch and a wss. Then wash and starch again.