should C++ class "helper functions" be members, free, or anon-namespace free?

Free function / member function

I would make them free functions is possible (they do not need access to the internals of the class). If they work on a set of attributes or need access to other members then make it a member function.

Access

If the code only has sense in this scope, and will not be used from other code then make them private: private if it is a member, or implemented in an unnamed namespace if it is a free function.

If other code will benefit from using the code then publish it in the interface. That means making it protected if it is a member or having the free function accessible through a header in a named namespace (or global namespace).

I generally make helper routines "free" routines in an anonomous namespace if possible. That way I don't complicate the interface (off in the *.h file) with stuff clients don't need to worry about.

However, you have to be careful that you don't introduce non-reentrancy by doing that. For instance, by modifying global data objects or static locals rather than class members. If you need to do that, you are better off making it a proper class member.