However, he does a good job of giving a basic introduction and framing for Stoic concepts. I think it's easier to digest the Romans (particularly the concise and acerbic style of Epictetus) if you are somewhat familiar with the subject. I got much, much more from Epictetus than I did from Irvine, but he is, I think, a valuable on-ramp.
I'm also not sure what the big deal is with Marcus Aurelius. Compared with The Enchiridion and even Seneca's letters, it's haphazard and dull. I'll give it another shot once I'm done with all of Seneca's letters.
Personally, I would start with Irvine, then the George Long translation of The Enchiridion (it's more poetic than the Carter translation, IMO). I'm about half way through Seneca's Letters, and while enjoyable, he takes a long time to cover the same insights as Epictetus.
(aside: on my 3rd or 4th reading of The Enchiridion, I wrote brief notes on each part, which you can find at http://thiscodinglife.com/dissecting-epictetus/intro)