I used to prewash my fabric and use cotton batting.
Now I use the rinse and spin cycle for the fabrics. It seems to be enough. However, strong colors get a different treatment (reds, royal blues, blacks), because of the bleeding factor.
I have never prewashed or tried to preshrink a cotton batting. The wrinkled look doesn't do it for me anymore. I have old quilts from 3 generations...and now I'd like to switch to less wrinkled. I've tried Quilter's Dream Green. It's great, but I don't use it if there's a lot of white in the quilt.
Baby quilts have different suggestions from the manufacturers because of flammability. It's their way to protect from lawsuits. I make baby quilts and let the parents know the composition of the quilt. From there it is up to them whether to use it or not.
Welcome to quilting and to the QB. You'll find a lot of good advice here and will get to pick and choose what route to take on quilting. Enjoy!