For phone cards, your best option is to buy a cheap one of multiple types. I saw some that offered very low per-minute rates (some even billed in 1/10 minute segments). Test calls showed that the rates on many of the ones I tested were fake. The excuse was "taxes aren't included". I call BS on that for 2 reasons. First, these taxes varied wildly from card to card for calls between the same 2 cities. Second, after plowing through a pile of cards, I finally found one which charged just about exactly what it claimed, and was cheaper than the cheapest one after the undocumented taxes were added.
This was well over a decade ago and I don't remember any of the brands.
Skype can work in China. Another option is a Google Voice number. Setting one up requires (or required when I set it up) a US phone number that can receive a conformation code. Once its set up, you don't really need access to that number anymore.