How do you decide between passing arguments to a method versus simply declaring them as object instance variables that are visible to all of the object's methods?
I prefer keeping instance variables in a list at the end of the Class, but this list gets longer as my program grows. I figure if a variable is passed often enough it should just be visible to all methods that need it, but then I wonder, "if everything is public there will be no need for passing anything at all!"
Since you're referring to instance variables, I'm assuming that you're working in an object-oriented language. To some degree, when to use instance variables, how to define their scope, and when to use local variables is subjective, but there are a couple of rules of thumb you can follow whenever creating your classes.
Instance variables are typically considered to be attributes of a class. Think of these as adjectives of the object that will be created from your class. If your instance data can be used to help describe the object, then it's probably safe to bet it's a good choice for instance data.
Local variables are used within the scope of methods to help them complete their work. Usually, a method should have a purpose of getting some data, returning some data, and/or proccessing/running an algorithm on some data. Sometimes, it helps to think of local variables as ways of helping a method get from beginning to end.
Instance variable scope is not just for security, but for encapsulation, as well. Don't assume that the "goal should be to keep all variables private." In cases of inheritance, making variables as protected is usually a good alternative. Rather than marking all instance data public, you create getters/setters for those that need to be accessed to the outside world. Don't make them all available - only the ones you need. This will come throughout the development lifecycle - it's hard to guess from the get go.
When it comes to passing data around a class, it's difficult to say what you're doing is good practice without seeing some code . Sometimes, operating directly on the instance data is fine; other times, it's not. In my opinion, this is something that comes with experience - you'll develop some intuition as your object-oriented thinking skills improve.