Working viza for Estonian citizen living in the UK

Hi. I intend to work in China as a teacher for 2 years. I am Estonian citizen but live in Uk. My School suggested to prepare Police check and medical check for getting residence permit.
from which country should the police check be done: from Estonia or from England?
How, where and by which embassy should these documents be legalised.
What will be cost of Z viza for me?

Thank you