I am currently creating a utility class that will have overloaded operators in it. What are the pros and cons of either making them member or non-member (friend) functions? Or does it matter at all? Maybe there is a best practice for this?
Each operator has its own considerations. For example, the << operator (when used for stream output, not bit shifting) gets an ostream as its first parameter, so it can't be a member of your class. If you're implementing the addition operator, you'll probably want to benefit from automatic type conversions on both sides, therefore you'll go with a non-member as well, etc...
As for allowing specialization through inheritance, a common pattern is to implement a non-member operator in terms of a virtual member function (e.g. operator<< calls a virtual function print() on the object being passed).