I've done a lot of onesies. I use a cutaway stabilizer on the back and I always use a piece of water soluable stabilizer on the top. This keeps the stitches "on top" of the fabric, vs. them sinking down into it. I use Sulky's Tender Touch on the inside of the project when I am done. This covers the stitching and is soft against a baby's skin.
Here is a tutorial from Embroidery Library. It's a blow-by-blow on how to embroider on a onesie. They have tutorials for practically every fabric/project you can think of.
http://www.emblibrary.com/EL/elproje...log=Elprojects