If you want to have a richer understanding of the Stoic philosophy, it's time to read Diogenes Laertius's Book 7. Diogenes wrote The Lives and Opinions of Eminent Philosophers, one of the great resources we've used to reconstruct ancient philosophical beliefs. In Book 7, Diogenes covers Zeno, the founder of Stoicism. Book 7 gives a detailed explanation of stoic thoughts on Nature, Logic, Ethics, Goodness, Virtue, the evaporation cycle, and how eyeballs work. Seriously, it gets into detail. The great thing is, Book 7 is free online and it's not an extremely long read. Diogenes provides us with unique insight into the Stoic system. Bookmark it, then read it, because the Enchiridion is not enough!
Seriously, the Enchiridion is not enough. Neither are Marcus Aurelius's Meditations or Seneca's letters. Epictetus's Handbook, as compiled by Arrian, is a Cliff Notes version of Stoicism and an incomplete one at that. It's basically the sort of thing that would be handed to First Years at Hogwarts. Here's some basics, stay out of the way of the big kids, and no you can't take Defense Against the Dark Arts yet! Epictetus's Discourses give us much more, but those lectures assume a framework of knowledge in the audience that we aren't given access to (except through Diogenes). Marcus Aurelius is journaling his personal experience as a Stoic, which is illuminating, but he's not laying out a philosophical framework. He's attempting to live within that framework. Seneca...well he has a lot of good stuff! Diogenes is a quicker, more concise read. Also, Diogenes is laying out Stoic thought simply to explain it. Whereas Seneca is presenting his own ideas; Stoicism with a flourish. So dig into Diogenes. A quick read will be helpful. A second and third pass will acquaint you with how very particular, and peculiar, Stoic thinking can be. Bonus: the natural sciences comments are a riot. One minute Stoics are correctly explaining eclipses, the next they're talking about how earthquakes are caused by underground winds. Good stuff!
*I replaced earlier online versions of Book 7 with the one above after it was pointed out by the Reddit user MindfulMonk. It's in a much more useful format and I'm thankful to know about it.