My choice would be Mountain Mist Blue Ribbon 100% cotton batting, but this is an extremely traditional choice. It is a thin cotton batting with no scrim. I used this in the very first baby quilt I ever made and had a chance to observe the quilt again about 18 years later. The binding was worn at the edges and the fabrics were softly faded, but the quilt itself was soft as a cloud. Cotton gets softer with every washing. It was interesting to see how lovingly the grown-up owner handled this quilt, which was brought out for special occasions when she was babysitting her nieces. This batting requires close quilting (no more than 2" apart). Although I hand quilted that one, machine quilting would be fine too. I would choose a lightweight thread for the quilting so as not to add any stiffness -- probably Aurifil 50wt 2-ply thread or Glide 60wt polyester.
I believe Quilter's Dream 100% cotton in request weight would yield a similar result but require less quilting.
My preference would be to stay with a thin batting because it keeps the quilt very flexible (for wrapping around an infant). Hobbs Polydown could be another good choice, especially since it dries fast, but might not be quite as flexible because of the loft. I personally stopped using Warm and Natural because, compared to the battings mentioned, it is has a fairly stiff drape -- especially when new. It does soften up with repeated washings, but needlepunching through scrim is probably always going to contribute some stiffness to a batting. Quilter's Dream is needlepunched for stability, but not through scrim, so I think would be more drapeable from the get-go.