Currently, most foreigners in demand in China are English teachers, and these offers are mostly provided by schools. Schools are classified into public schools and private schools. A few private schools promise a high salary in advertisements, however, after having worked there you may find out that a few private schools couldn't arrange a Z or F visa for you to work in China, and it would be difficult to get the entire salary they promised before, for reasons that they don't take in enough students or the quality of you classes is not good enough. And of course, it is illegal to wok in China without a Z or F visa, while in public school, there is a Foreign Affairs Office that will assist you in your work and daily life, provide better accomodation for foreign experts, and the salary is paid entirely according to the contract. Moreover, there won't be too many classes, and you could enjoy all the holidays set by law as well. Of course, these public schools will offer you Z or F visa and Certificate of Foreign Expert.
Advice: Like most people, try to apply a job in public schools. It is true that not all private schools have a poor credit, but before accepting invitations from any employer, you should be recommended by a foreign teacher who has worked there, or have a perfect contract with them.