I encourage you to not worry about centering - instead, plan it to be off center and/or off kilter (as we used to say). That way you don't have to worry about whether anything moves. When I enter a square or rectangle, I first put on borders that are actually triangles so the square/rectangle is "a-kilter' then put the other fabric around it with straight seams.
and like others have said, be sure to have wider backing than the top and batting - if you use a long-armer they often require 3 to 4 inches on every side...so add 6 to 8 inches to both length and width.