Look at the Quilters Dream website for some ideas. They are the makers of the green which I haven't used myself but others seem to like it. They also make one called Angel that is fire retardant, if that is a concern for you. I use Quilters Dream batting for most all of my quilts and I prefer to use the all cotton bats. The majority of the quilts I've made have been for my grandkids and kids and so far no problems that I know of. I use Aurifil thread for piecing and quilting. I think the problem thread that you are thinking of is the invisible thread that some say can come lose and wrap around a tiny toe or finger and is hard to find. Personally, I would not use it on anything but a wall-hanging.
Have fun with your baby quilts! They are a favorite of mine!