You seem to be mixing up two different concepts, copyright and licensing.
As a photographer, you own the copyright for images you create (unless you have other contracts which override this, such as a work for hire agreement). The only other action to take regarding your copyright is optionally registering as such (which is usually optional).
Your main question here is regarding the licensing of your work. It is possible to offer multiple licenses for a single work (a non-exclusive license). This is the default, so you are able to offer a creative commons license for non-commercial use, then also offer a separate license that allows commercial use. In this way, you can make a profit on commercial use without charging someone for personal use.
Some stock sites will require an exclusive license, meaning that you are agreeing to only provide a single license of your work.