The agency you choose will determine what you can or cannot do with regard to being independent vs shop affiliated. Most allow independent instructors, but SSI, for example, does not. It will also determine under what standards you are working. Standards vary greatly from one agency to another. Some require lots of skills, other do not. Some allow you to add requirements to your class, others do not. Some have a very rigid structure, other allow their instructors more flexibility. All of these factors can be seen as an agency's philosophy of their approach to teaching people to dive. While there are very strong opinions as to which approach is best, the important thing is to certify through an agency whose philosophy more closely matches your own.
Personally, I like lots of freedom to teach skills in the order I think best, I like to be able to add requirements to my classes, I like high standards. For these reasons, I chose to be a YMCA SCUBA Instructor. I felt we were a very good match. Your philosophy may differ, go with what's best for you.
