I've been teaching Aristotle and Hume (along with Plato, Kant and Kierkegaard) in an Ethics course for non-philosophers at the technical university where I work. Usually I like to teach Nietzsche when teaching Ethics, and reflecting common practice at present, the Genealogy of Morality. Usually I use the Walter Kaufmann edition, but I have also used the Maudmarie Clark and Alan J. Swensen edition. This semester I've give Nietzsche a rest, largely because as my students are not philosophy students they are more likely to pick up on the 'Nietzsche was a Nazi' myth. They are very good science students, but they lack a context to distinguish unreliable rumours in philosophy from genuine interpretation. I'm sure I'll go back to Nietzsche again in a course where I'll think of the best possible way of dispelling the infamous myth, but I'm having a break to get perspective at present.
Aristotle and Nietzsche
In teaching these philosophers I am certainly thinking about Nietzsche at all times (so it's not really cheating on Nietzsche). One thing I'm concerned about is the assimiliation of Nietzsche to Aristotelian Virtue Theory. It's a productive exercise t put Nietzsche in the context of Aristotle and Neo-Aristotelian virtue theory, but the differences are important. There is a bestowing virtue in Thus Spoke Zarathustra, but it is egotism. It is true that Aristotle's virtue is egotistical in some way. As with other Antique thinkers, he's concerned with the health of the soul, rather than assuming a burden of moral obligation. But, the Aristotelian Virtue is learned over time and becomes habitual in cognitive process with feed back as immediate knowledge of a principle becomes habitual knowledge of how to follow a principle in practice. But in Nietzsche virtue is the expression of a self which does not accept external legislation. It may be tempting to think of Nietzsche's 'Overman' in terms of the 'Magnanimous' or 'Great Souled Man' in Aristotle. However, the Great Soul man is understood through the mean between excess and lack of virtue in Aristotle. Aristotle prefers the excess of virtue over the lack, so this does lead to some Nietzschean looking thoughts on the virtues of giving and heroism. The Nietzschean Overman experiences great tensions between great conflicting forces and has to be strong enough to integrate them. The Great Souled man follows prudent habits in which we have a set of consistent virtues, which connect with no problem. Nietzsche's ethics must be understood in terms of self-invention, inner conflict and a spontaneous giving from bursting inner strength; together with a strong distinction between inner life and civic life.
Hume and Nietzsche
There are readings of Nietzsche which make him look like Hume based of the claims that both Hume and Nietzsche are: determinists with regard to the will; have a naturalistic view of philosophy and mental contents; follow a empirical-scientific model for philosophy. I doubt that Nietzsche read much Hume, his reading of the history of philosophy was patchy. He knew the Greek and Roman texts very well, and had only seriously read later philosophers in an intermittent way. This is used as argument against reading him in the context of Kant and German Idealism , but strangely not Hume. I suggest that his idea of Hume, as part of a group British psychologists, largely derives from his friend Paul Rée. The empirical-scientific model in Hume is very subjectivist-empirical undermining the objectivity of science, but that seems to be overlooke din the Humean Nietzsche readings. Nietzsche did not abandon an earlier 'aesthetic' view for a later 'scientific view', as he sees continuity between science and art. Hume's ethics of minimising pain and increasing pleasure is reactive by Nietzsche's standards; Nietzsche's ethic is one of a strength which can absorb pain and which creates without regard to a calculus of pain and pleasure; the creative uses and increases pain to increase. It seems to me Nietzsche does have a form of libertarianism with regard to the will, based on the indeterminism of nature; and one might argue Hume shuld have done the same if he had been consistent about the invented nature of causality.
Nietzsche, Kant and German Idealism
This whole topic has fallen into undeserved oblivion. It's true that Nietzsche is against the Idealist view of a strong homology between mind and nature. It's may also be true that Nietzsche's main understanding of Kant was through Schopenhauer's reading, and that he had not read much German Idealism. With Nietzsche though, it is important to realise his talent for strategic reading, on the basis of limited knowledge he was able to grasp the significance of Kant and Hegel for his own ideas, and the conflcits he was interested in. The section on duties to oneself in Kant's Metaphysics of Morals, refers to the human as the individual who commands and obeys the self. This is a very Nietzschean thought, the human strength which grows from inner conflict. The Kantian self legislates from a subjective point of view, it's good for Nietzsche, though the universality of reason is not so good for him.