Readings in Classical Chinese Philosophy is a great little collection of some central texts, with minimal but helpful commentary. Some, like the Analects and the Daodejing, are short enough to be printed in full, and others have selections.

For Indian philosophy, I don't have any immediate recommendations. I've heard good things about Edward Conze's books on the history of Buddhism, but have never read them myself. Odds are they might be a bit dated, but still a strong introduction.

For a general overview, Peter Adamson's podcast and book series History of Philosophy Without any Gaps is usually great, and his strong suit is in medieval islamic thought.