Aristotle had a some still-relevant thoughts about happiness, and what one should or shouldn't do.
Nicomachean Ethics is his study of the question, and remains a cornerstone of Western
moral philosophy, 2300 years later.
That we "should" pursue happiness, there can be no question. We humans are designed around satisfying our hungers, up Maslow's heirarchy of needs from such blunt necessities as food to such subtle satisfactions as wisdom and virtue. It's a philosophical fundamental that things "should" do as they're designed. I think Aristotle would have been comfortable with the notions that "being happy" is not so much a mental "state" to be turned on or off at a whim, but rather a rational appreciation of personal achievement; and that satisfactions further up Maslow's scale are more valuable than the basic daily human pleasures of sleeping and eating. So, I "should" be happy to the extent that I'm pursuing the fulfillment of my needs, particularly such lofty desires as virtue and wisdom.