Hi and welcome to the board.
You need to preshrink your batting as well if you don't want any puckers at all. Read this blog by the late, great Sue Garman.
http://suegarman.blogspot.com/2013/03/
Additionally one hot water wash to preshrink your fabrics won't fade them as long as they are good quality fabrics. And a hot water wash will go a lot further for releasing any excess dye that may be in the fabric than cold.
If you don't want any puckering in your finished washed quilts prewash/preshrink all your fabrics, top and backing fabrics in hot water and tumble in dryer. Preshrink your batting as per the blog link I provided. (also in hot water and tumble dry until almost dry)
Once you wash your completed quilt in cold water block it as Tartan mentions. This means drying flat stretched out and held in place with pins, lots and lots of pins.