I agree that this is an amazing job for a first quilt! Great job. I prefer 100% cotton batting myself. For all, not just baby quilts. It will tend to give the 'crinkly' look when washed as it does shrink. Most cotton battings, I don't believe, lend themselves to being pre-shrunk. I use Warm & Natural as I have an entire roll of it, but if not, would probably go with the Quilter's Dream brand. It does have a very nice drape and hand to it. W&N allows quilting up to 10" apart. Not sure of other batts, so you may want to check out that aspect as well, once you've determined your quilting pattern.
As to border...I might go with a lighter color, just to pick up some of those shades and make them 'pop' a bit. With the job you've done here though, I'm sure anything you decide will be lovely.