Adding to John's answer, which has all the important info about the three categories you mention.
You wonder about Creative Commons. They are a set of copyright licenses (not an alternative to copyright, they work alongside it). The 'advantage', so to say, is you can choose your copyright terms to best suit your needs.
Some of the most used CC licenses are:
Attribution
Lets others distribute, remix, tweak, and build upon your work, even commercially, as long as they credit you for the original creation.
Attribution-ShareAlike
Lets youothers remix, tweak, and build upon your work even for commercial purposes, as long as they credit you and license their new creations under the identical terms. This license is often compared to “copyleft” free and open source software licenses.
Attribution-NonCommercial
Lets youothers remix, tweak, and build upon your work non-commercially, and although their new works must also acknowledge you and be non-commercial, they don’t have to license their derivative works on the same terms.
Attribution-NoDerivs
Allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to you.
And then you have some combinations of the previous (like Attribution-NonCommercial-ShareAlike or Attribution-NonCommercial-NoDerivs). You can see the whole list here.
In your case, because you want to use images for commercial web, an Attribution license would be enough (as long as you mention the author somewhere in your project). The only materials you cou;dn'tcouldn’t use would be the NonCommercial ones.