stitch in the ditch around the squares. This will stabilize it for when you do the quilting. the more square quilting design looks better than the other more circular designs. pin and pin as you quilt. Even tho I may have basted the quilt, I still use the long yellow pins in front of the pressure foot to help hole the layers in place.
You might also consider varigated thread. This will give texture rather than new design and will less noticable. It has already been suggested, but it appears that you need more practice to get curves more even and the long lines straighter and more even. ......and go slow. Don't try to be fast. There is more control. And any time you feel you are loosing control of the quilting - such as needing to move hands, stop with needle down and regrip and then begin. Always leave needle down. That way the quilt doesn't shift as you are repositioning. Then when you start up again, let the needle got up and down a couple times in place until you feel you have control and ready to move out.