The Chinese staff will take you and do it together with you at the bank.
To set up the bank account in China, technically you need to have the residency permit, but it is still possible for most areas to help get your bank account right away. It is helpful to have your bank account quickly so that you can start using Wechat pay or Alipay (both are similar to Apple Pay). These are definitely used more than cash or credit cards and more places are started to not accept cash.
The amount of time for the process really depends. This has been done in as short as 20 minutes and as long as a few hours.
In the rare case they cannot get it set up for you before payday, your first payment from the company would just be in cash.
It is not clear the differences between the banks. (If anyone has more information on differences, please let use know)
Usually you will set up your bank account at the bank that the Chinese staff uses or is closest, but if you have a preference, it should be fine to help set it up where you want.
Banks do not really connect well with banks outside the country (for the customer at least). For example, HSBC seems to have banks in all countries (it is harder to find ATMs inside China) and there seems to be no benefit for transfers with no additional ease of use from having an account at HSBC in a number of countries.