I was speaking with some of the current teachers at my future employement and they specifically told me not to get the medical at home cause I MUST get one in China to finalise the visa and work contract. My employer sent me a list of things for me to have before I come, singed contract, passport with 6months, etc... and medical certificate with X, Y and Z. I asked what is the point of it cause I'll be getting it done in China anyway. They said they want to see my health certificate, it is not part of the visa application, it is just for the employer to see, only the health check in China is actually needed for the visa because you have to qualify for medical insurance. Anyway, I told them I'd go for a basic checkup and send them a letter from my doctor saying that I don't have any diseases, health issues and am not on any medication. Note that is it fine for you to have some issues with you health that your employer need not know about, but it was easier and free-er for me to just send that letter to make them happy.