If you have a Chinese business partner, who is not family, do not give them full access to your bank.
Do not trust lawyers unless they are connected to your family (requires a Chinese spouse).
Training centre is do-able, but a 'school' requires a special licence that you will not get. However you can operate off another schools licence, but they can want too much 'rent', perhaps 15-20% of turnover (not %of profit)
You can set up as a consultancy, the easiest way to do it. Your scope of operations must be vague as your licence will not allow anything not in your scope, e.g. you cannot do translating as an official business, unless you are qualified in China.
You can set up as a WFOE, that way you are not employed by your company, as employing foreigners requires a special licence.
You need a sum of money (100k RMB?) to lodge with a bank as registered capital. You also need to set up with the tax office. This costs money.
Every city has a Director in charge of Foreign Investment. Once you are sure you want to set up a company, go and see them. If they are below target they can (if they chose) bend over backwards to help you through the admin quagmire. Alternatively they may be the first in the line of people who want to fleece you.
Your negotiation anchor should be that you are looking at several cities in which to invest. This implies that you can easily walk away.
Remember that the business culture in China has a different focus. Everyone is cost focussed, and will haggle you down on your prices and will charge you more if they can.
People go into business for what they can take out of it (today), not what they can put into the business for tomorrow's gain. This is important to remember if you have partners, you may be struggling to feed your family, while your partner drives around in a new BMW (seen it).
In the words of Fox Mulder, 'trust no one'. Especially not partners, lawyers and accountants. Unless they are family.
Many people in quieter districts/cities teach from home unofficially, marketing is by word of mouth. If you get a visit from an official, unlikely, you can offer free classes to their kids. Or take them out to dinner and get them very drunk on Moutai (expensive baijiu).
General rule. The further from the big centres you go, the less officialdom, the more corruption, the smaller the 'gift' expected.
There are several articles on setting up business in China if you want to do it officially. Unless you want to build a brand and grow it is probably not worth it. Point to note. All the big brands are now struggling. The market is rapidly maturing. Fees are coming down and teachers pay has not gone up significantly in 10 years.
Employing people can be another nightmare, as every employee holds your reputation in their hands.
All of the problems I mentioned can be overcome, but you need to go in with your eyes wide open.