I'd recommend a couple of classics, both accessible to non-specialists:
The Great Chain of Being is a nice overview of some of the main themes of ancient metaphysics and their later influence.[1] It ranges far beyond the ancient world, but it does as good a job as anything can of showing how ancient theories that might easily seem conceptually alien could in fact have been rational.
Shame and Necessity is about what you might call the ethical mindset of the ancient world.[2] The general aim is to explore how the ways Greeks and Romans engaged with moral questions systematically differed from what ethics would become after the advent of Christianity. (I can't praise this book enough. Williams was insanely erudite and analytically sharp.)
[1] https://www.amazon.com/Great-Chain-Being-Study-History/dp/06...
[2] https://www.amazon.com/Shame-Necessity-Sather-Classical-Lect...
If you want to follow the above approach I think the best resource is the fantastic Philosophy Bites podcast (http://www.philosophybites.com/) where philosophers are interviewed. And if you're more of a printed matter type of person, they have books with the transcribed interviews, too (https://www.amazon.com/Philosophy-Bites-David-Edmonds/dp/019...).
This, I think, is a great way to identify the areas of philosophy you're interested in to zoom in further.