One of the questions I'm most commonly asked is "What books should I read first?" Here are my recommendations. I've tried to steer people toward books that I know are reliable as an introduction. I'll leave it up to you, though, whether you want to begin with ancient or modern books on Stoicism.
I would normally recommend that most people begin by reading The Meditations of Marcus Aurelius. That's traditionally the most widely read book on Stoicism. The most readable modern translation is by Gregory Hayes.
Then I'd suggest reading The Handbook (Encheiridion) of Epictetus, in Robin Hard's translation. It's a short book. If you like Epictetus, you may want to read his longer Discourses. If you want to read more classical Stoicism, the next on your list would normally be the Moral Letters (Letters to Lucilius), of Seneca.
I wrote a Teach Yourself book called Stoicism and the Art of Happiness, because people were asking me for a step-by-step guide to Stoicism in the form of modern self-help. Other books I would recommend for complete beginners include The Daily Stoic by Ryan Holiday and Steven Hanselman, How to be a Stoic by Massimo Pigliucci, and A Guide to the Good Life: The Ancient Art of Stoic Joy, by William Irvine.
I don't know if I'd describe it as a beginners' book but The Philosophical Regimen by the Third Earl of Shaftesbury is one of my favourite books on Stoicism. Not only does it serve as a great commentary on Epictetus and Marcus Aurelius but it's a great piece of Stoic literature in its own right. If you really love The Meditations of Marcus Aurelius, you should definitely read The Philosophical Regimen as well.
The Inner Citadel by Pierre Hadot is really an academic analysis of The Meditations of Marcus Aurelius but it's pretty accessible and one of the most loved books on Stoicism by a modern author.
Thoughts of a Philosophical Fighter Pilot by Vice Admiral James Stockdale is also much loved by modern Stoics. Stockdale relied on his memory of Epictetus' Stoicism to endure years of torture in a North Vietnamese POW camp. (He later ran as an independent vice-presidential candidate in a US election.)
Here's a link to a GoodReads list called Beginners' Books on Stoicism, to which I've asked my Stoicism community to add their favourites recommendations. Please add your own suggestions to this list and in the Discussion area below.