As mmj suggests buying a separate SIM card for each country is the easiest and likely cheapest option. Buying one card to access different Telecom providers in different countries (roaming) can be expensive, speaking from first hand experience. I use local SIM cards for use in NZ, Australia, Ch!na, Malaysia and Thailand. It's a pain to have to carry and swap out SIM cards each time I travel to said countries, but it is a matter of cost versus convenience. Buying a SIM card is easy in Thailand and Malaysia, whereas buying a SIM card in Ch!na requires ones ID card/Passport etc. In Australia, NZ, Malaysia and Thailand, there are various SIM card options sold at the arrivals section of the international airports.
Also anything related to G00gle in Ch!na, will require a V P N that works. Keep in mind that sometimes V P N also have issues... as there are local authority "crack downs" from time to time (cat and mouse / carrot and stick 'games').