Hermes, the Greco-Romans in general do not talk about happiness, they talk about eudaimonia, the life worth living. The modern research on happiness shows that it is a mushy concept, and that the explicit pursuit of happiness is a major cause of unhappiness.
Also, Stoicism has nothing to do with puritanism, since for the Stoics pleasure is “in accordance with nature,” and therefore can be selected.
Obviously it is up to you whether to embrace Stoicism or not. That said, my new book, coming out 9/15, in part addresses the issue of how to update Stoicism for the 21st century: https://www.indiebound.org/book/9781541646933