I'm currently working for at the company that just offered you a job. This is what I can tell you...

1. They have never been late on paying me or any other teacher their salary.
2. The salary agreed upon in the contract is exactly what they pay you (after tax has been deducted).
3. They do give you a Z visa.
4. Your ability to rise within the company depends on your ability to prove you're worthy of a promotion. This company hates entitled people. If you're willing to work, they are more than happy to keep you and reward you.
5. Time Education China.... is just the parent company that owns Elan School.

Things you should know before coming to China (if you haven't already been told):

1. This IS China. Take every preconception you have of how things should be and throw it out the window. Its a different culture and a different country, and understanding that they do things differently here will make your stay much more enjoyable.
2. Although rent is not very expensive per month, the large single payment you have to make to rent a place can be. In Beijing its usually (5 x monthly rent) for the first three months. It breaks down to 3 months rent for the first three months, plus 1 month rent for deposit, and 1 month rent for the agency fee (for helping you find the place). So bring enough cash to last you until your second paycheck.