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. If you were to take this route, you would not be able to also provide a creative commons licensed version.
Also, it is important to keep in mind that the licenses you provide are by default a permanent agreement, meaning that you can not simply change the licenses you have provided in the past. This means that any images that you have previously released under a creative commons license are no longer eligible for exclusive licensing, but you would be able to offer a non-exclusive license.