I'd consider myself secular/agnostic myself, I just agree with the philosophy.
For Taoism/Daoism, start with the Tao Te Ching. Translation issues aside, it's really short and gives you a basic understanding of the general tenants. If you have trouble with intreptation, auxiliary resources could help like on youtube or through lecturers. (Allan Watts is probably the most famous) I'd recommend getting used to terms like "Wu Wei" and "the Dao" because it makes for good short-hand for studying. Also doing research into psychological fields alongside it can help if you want to get into a more secular version like me. (Mihaly Csikszentmihalyi-which I found out ironically from an episode of EFAP-covers the psychology of "flow" which is what Taoism seeks to encapsulate in "wu wei.") I also, although have yet to read it, would recommend the Zhuangzi as a series of examples.
Buddhism is a little more complicated due to the many branching sects and faiths. I'd start with reading the history and the various anecdotes foremost, as well as getting the basics down like the Four Noble Truths, Eightfold Path, etc. It started in direct opposition to Hinduism as a more liberalizing and egalitarian force, accepting men and women (initially-depends on the sect) and saying any one of any caste or people-perhaps even of any religion-could achieve a state of Nirvana-or Non-existence- in one lifetime as opposed to the many to reach the Brahmin caste of Hinduism. Understanding the history would probably give you the best insight into the different sects like Zen, Mahayana, etc.
Buddhism is interesting because the original teachings were quite agnostic and didn't mention a god or good and evil so much as how to limit suffering and reach a state of inner enlightenment and peace by removing all attachments and self-centeredness and to move beyond oneself.
Probably the most famous piece of Buddhist literature is Journey to the West, but that's dense as fuck and wouldn't really give you a clear picture if you didn't know what you are looking for. The Sutras and other older texts are either untranslated or like reading the bible dry so I'd avoid just jumping into the fire directly if you catch my drift. (We also talked about the history in the Philosophy Thread if you want to see us shitposting a lot.)
@Zephyrus
I should note that Avatar: The Last Airbender (The Good one) actually reflects some Confucian notions like Filial Piety, Mandate of Heaven, etc. in Zuko and Iroh whilst their relationship to their father/brother respectively shows the inverse of how Confucian believes a ruler should rule a nation and how people should treat their families. Food for thought.