This book by 19th century German scholar Eduard Zeller got me started on Stoic and Epicurean philosophy over three decades ago, and the two philosophies have enriched my life ever since. They are both practical and easy to understand, and they can help anyone get through the difficult periods of their lives. While I have never been interested in the third system Zeller writes about, Skepticism, his analysis of both Stoicism and Epicureanism are probably the most brilliant ever written.
All of which means, in my opinion, that this is the first book you should read about the two systems. Most contemporary interpretations of both Stoicism and Epicureanism strike me as either prettified or inaccurate, and they seem to be aimed at giving the reader some kind of spiritualized ego-gratification, instead of the kind of self-awareness and self-discipline necessary to bring about a meaningful personality transformation. But a careful study of the surviving Stoic and Epicurean texts, plus a book like Zeller's, can change anyone's life for the better. And while there is much information in Zeller's book which tends to drag, if you are willing to persevere with the text until the end, you will find much practical advice about how to live a tranquil and contented life, something which is needed today as much as it was over two millennia ago.
Throughout the book Professor Zeller takes care to emphasize the differences between the three systems instead of the similarities. However, given the fact that Stoicism developed out of Epicureanism, there are definite resemblances. I recommend that instead of limiting yourself to one particular School, you should take what you find valuable from each. For example, Stoics have no place for the needs of the body in their system, while the Epicureans reject the idea that human consciousness can survive after death. In my opinion, a well-rounded human being should allow for both. So perhaps the best way to follow these philosophies is perhaps the idea of a stoicurean. A good stoicurean will not only acquire the ataraxia (ἀταραξία) necessary for inner tranquility but the apatheia (ἀπάθεια) needed to deal with externals as well. And certainly everyone in our attention-whoring world today needs to be reminded of the vanity of glory.
As you read the book it becomes obvious that the Stoics are Zeller's heroes; most of his criticism is reserved for the Epicureans and the Skeptics. But it is also interesting to see that Zeller is honest enough to admit that the Stoics actually approved of . . . divination! Well, in my opinion, the Stoic acceptance of divination is a point in their favor, not a weakness. But rationalist that he is, Zeller apparently must grit his teeth and make the best of it any way he can:
The highest business of philosophy is to reunite man with the divine world external to himself. In a system so purely based on nature as theirs, the supposition that God works for definite ends after the manner of men, exceptionally announcing to one or the other a definite result--in short, the marvellous--was out of place. But to infer thence--as their opponents, the Epicureans, did--that the whole art of divination is a delusion, was more than the Stoics could do. The belief in an extraordinary care of God for individual men was too comforting an idea for them to renounce; they not only appealed to divination as the strongest proof of the existence of Gods and the government of Providence, but they also drew the converse conclusion, that, if there be Gods, there must also be divination, since the benevolence of the Gods would not allow them to refuse to mankind so inestimable a gift.
This makes perfect sense to me.
If you are interested in exploring these subjects further, there are two Reddit discussion groups about Stoicism and Epicureanism, both of which have excellent links to online resources. There is also one other book about post-Aristotelian philosophy which I can recommend: Philosophy as a Way of Life: Spiritual Exercises from Socrates to Foucault (1995), by Pierre Hadot.
Read The Stoics, Epicureans and Sceptics here