Hi Sarah,
Welcome to the board. As Grammashel said, Fat Bat is really not the best batting for hand quilting. That type batting is more suitable for tying the quilt which will also look lovely as well on your pretty quilt. You could tie it with a mix of blue and pink embroidery floss.
I think what you first need to do is decide on your quilting so you can guage how far apart your quilting is going to be and base your batting selection on that. All batting states on the packaging how close your quilting must be for that particular batting. I find polyester battings are the easiest to needle but have also handquilted 80/20 blends quite successfully. Wool is supposed to be the best for handquilting but it is very expensive. I myself have never splurged on a wool batting.
As far as brand is concerned, My experience with Mountain Mist polyester batting has not been great. The fat bat is fine but the lower lofts tend to be a bit inconsistant in thickness and pull apart very easily they are easy to quilt but fragile and I have had the batting come apart near the outer edges of a quilt in the sandwiching process or just from handling the quilt in the quilting process, very disappointing. Fairfield is a bit better but when it comes to polyester bats I really, really like Quilter's Dream or Hobbs. These bats are more expensive than Mountain Mist and Fairfield and I have never seen them at big chains like JoAnne's or Walmart. So you may have to go to a quilt shop or buy them on line.
As far as quilting ideas, the sky is the limit and what you feel comfortable doing. I would do small feather wreaths or a flower in the center diamond if this was mine. Then echo stitch 1/4" away from seam lines on the other pieced elements like the triangles that form the points of your stars. In the blue sashing I would quilt a leaf and vine or a cable design. You could go to your local library and see if there are any quilting books that give patterns so you can trace them to mark your quilt top. Please make sure to post pictures as your progress.