The primary qualifications for getting a teaching job in China are:
1. Being white (because only white people are Americans. There are no Chinese Americans, African Americans, etc.)
2. Having a pulse
Both qualifications are only the "ideal" situation, and the schools will work around them, accordingly.

Teaching at private institutes usually pays more money, but they are more demanding, more sneaky and diabolical (and when you say more sneaky in China - it carries some weight!), and will expect you to do the whitey the clown thing to a much greater extent.
I would reccommend working at a college. It's easy to get those jobs, and they're available everywhere you would want to live.
Check out anesl.com for some good opportunities, and as head hunters go - they're not the worst.
Payment for college teaching in most provinces not on the east coast is usually about 4k rmb a month.
Payment at most training centers is between 4k-8k, easily.
With the colleges you get at least a month of consecutive vacation at least twice a year which is very nice. At the training centers you don't, and work nights and weekends to facillitate your students schedules.
Colleges generally have much better guanxi with the PSB and can make things happen much easier.
Don't worry so much about your contract, because it's like a polite joke, at best. You'll sign 3 of them. A contract in Chinese, a contract in English, and the official contract used with the government for the purposes of tax evasion.
I've worked in China, South Korea, Thailand (and not teaching) in India for the past 10 years. If you have specific questions about this there's a good chance I've run into it before.
China is a cool place.
It's very cowboy still, and - I said something about this to Cameron the other day I think. . .
Chinese people generally are exceptionally friendly and giving if they know you. If you're a stranger on the street they are rude and selfish in ways that will shock you. Just learn to let go. Of everything. . . .
The thing is that Chinese people aren't intentionally trying to treat you badly and if you get to know them, even in a very informal way they are very very nice.
South Koreans on the other had are a different matter, and I refuse to even buy products like Samsung or LG that are branded out of that country.
It's not bad, I think.
Just be aware that the business culture is WAY different than in the West. Keep in mind that Mao Zedong, even now was still "70%" right in stealing everybody's land, killing them, having their sons beaten and re-educated until the renounced their families, etc. and understand that you will never win in any, any, any kind of disagreement with Chinese people in China, short of brute force.
Forget about your ideas of personal intergrity, learn to smile, say "maybe" and "I'll try" when you really mean "no", completely let go of your attachment to your personal space, etc. and you'll be fine.
Understand that more so than at home, people won't listen and will hear only what they want to hear - even if they completely understand the words you're saying.
Like:
"Allowing these children to refer to me in the first person as "laowai" rather than Teacher, Mr., Bill, Bob, Joe, or Lao Shi is completely disrespectful"
"Oh, you mean that you would like more chalk in the classroom?"
haha
Everything will be pretty cool for 6 months. After 6 years you understand the difference between the adventurist expat and the permanent expat, and that cross-cultural understanding and tolerance is basically a one way street of complicity to nonsense on your part.
That all being said - I plan to be here indefinitely and don't want to leave.