Other stuff.
Location, location, location. If you are out of the city centre, transport can be a problem. Especially at night. If you think you need to be near other expats, bars, cafes, etc. look for locations near Yunnan Uni, Green Lake, or Beichen. Or on the new metro train routes.
Beware in outlying areas some campuses lock the gates at night. You won't be let in, or out.
Payment mechanisms vary between institutions. Usually money goes into a bank account they set up for you, and you get an ATM card.

Language schools
Pay is higher
Check, sometimes no flights.
No accommodation, but sometimes accommodation allowance.
Expect to travel between sites in the city. They will usually only pay for bus, not taxi.
Some students motivated, but many are just there to play and unless you want to teach under 10s as well as teens, be prepared.

Schedules change at short notice and you are not expected to say no. This gives the possibility of picking up overtime pay.

You must work evenings and weekends. You will rarely get this time off.

Parents are a big issue sometimes. You need to leave the management of parents to local staff as it gets political.

You have a lot of customer groups to satisfy. These include local management, your director of studies (foreigner), local admin and sales, parents, students. Most have conflicting interests. This is a high stress environment.
The management is very cost focus. Sometimes quality of teaching is a low priority. Teaching materials are fixed. As an absolute beginner, as long as parents don't complain, you can get away with more.
You, the teacher, are merely a cash cow. The pay for you is higher but prepare to be milked. It is a high pressure job.
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Chinese High School with special oversea programs.
The program will often be in a high school but in a separate wing and have its own admin staff and Principal or Director of studies.

Same as high school but the SS are usally in the upper quartile of academic ability. Teaching staff are a mixture of local teachers and foreign teachers. The curriculum is US/Canada/UK.
Accommodation is not always provided, but sometimes accommodation allowance is paid.
Good staff are very highly valued. Expectations on staff are high.

Pay is often better than high schools.

Parents have very high expectations. They are sometimes rich and unreasonable in their damnds, but leave this to local admin.
Exams are set and moderated externally. You have to invigilate and sometimes mark tests.

Chinese High School
Same as universities
Students may or may not be motivated, and the English levels in a class can vary dramatically. Teenagers may also be, well? Teenagers.
Exams are set and marked externally. You will be expected to set and mark periodic informal tests, at no extra pay.
Foreign staff are valued by management.

Other colleges.
These are usually vocational colleges. Some SS are highly motivated as they are from poor families. They may have failed GK due to not having access to a good high school.
The facilities in some of these places can be appalling.
Usually no accommodation or accommodation allowance.
Often no canteen. But there will be street vendors outside the gate.