will Spotify work in China
Maybe. But I don't personally know. Definitely check with some Spotify forum.
Streaming media in China is a whole topic unto itself. There are many and various emerging services here and they're already hugely popular locally. (None of which I use but which somebody must.)
and am I right in assuming I can find "good" speakers to stream the music?
Yup. Electronics markets are many and products are various.