After you have been hired we get into the exact details of what needs to be prepared here.
MEF helps by paying for teachers to fly to China so you do not need to worry about that expense and can also support with a loan when you get an apartment in China.
The company covers the cost of applying and getting your work permit invitation letter (what you need from China in order to get a working visa) while you will be responsible for preparing for the local documents needed and for getting your visa. The cost is going to change for each area and you will need to search your area to get exact cost of each. The general expenses include:
having a valid passport (if not you need to get one)
Getting visa photos (similar to passport photos)
Getting a police check/DBS and having that notarized(2x) and then authenticated by the Chinese embassy
Getting your diploma/graduate certificate notarized(2x) and then authenticated by the Chinese embassy