Not all print sizes fit to the aspect ratio of your sensor, its just a fact of life. 4x6 and then 8 x 12 will use your whole image, the others that you mention will require you to lose some of your image. That's why when I shoot a wedding I try not to shoot too tight knowing that this is likely to happen.
Input your desired crop size into the appropriate fields in the crop toolbar
and then drag out your crop on your image to see where you end up. If you are losing part of what you don't want to lose you might have to try and add more to your canvas size using some of the content aware tools.
There is no cut and dried rule on how you should crop. The "two thirds rule" is simply a guideline and not necessarily gospel.