ATM's are everywhere in these cities including major city transport stations. Is your credit union ATM/debit card on a network like MC/Maestro/Cirrus or Visa/Plus? If so, you shouldn't have a problem, and most US travelers with credit union-based ATM cards have no issues. When withdrawing cash, I always recommend doing so at an ATM connected to a bank branch during business hours---so in case the machine eats the card (rare), you can immediately go inside and have someone get it out. And the risk of getting counterfeit bills out of a machine is negligible. In China, major bank branches in big cities are usually open on weekends as well as weekdays. But do try to frequently assess your cash needs. Chinese ATM's do not charge a transaction fee but your own institution likely will, so best to take out fewer, larger amounts rather than daily. Chinese ATM's generally limit each withdrawal to RMB 2000 or 2500 (occasionally larger or smaller), but you can do multiple repetitive transactions subject to your home account daily limits.

Most likely you will be using Bank of China, China Construction Bank, ICBC, China Agricultural Bank, or China Merchant's Bank for your ATM withdrawals since they are plentiful. Some of their smaller branches in local neighborhoods may not accept foreign debit cards but most likely anything you will come across on main boulevards and in touristed areas will. Don't worry about finding HSBC or Citibank machines, they are few and far between in China, and don't help you save money on fees unless you happen to have premium accounts with those institutions. Likewise, don't bother opening accounts with these two unless you have other reasons for doing so. You'd be better off getting a Discover debit card since those also work with the ubiquitous China Union Pay system. All merchants/vendors have machines that take Union Pay (Discover) cards so one of these allows you to just debit as you would in the USA. We have a thread somewhere on this forum about this.

Hong Kong has good rates on exchanging HKD or major currencies to RMB, so if it makes you more comfortable to get to Shenzhen with some RMB already in your pocket, then just exchange cash notes while in HK, and that will get you started until you get into Shenzhen and get sorted. I've found best rates in lower Kowloon like around Chungking Mansion, at licensed moneychangers which are a legal and accepted part of the HK retail money scene, and usually better and less hassle than changing at a bank.

How much cash RMB you actually need depends on your spending habits and especially if you will need to pay for accommodation as you go, or will be using prepaid reservations or credit card payment. Accommodation tends to be the biggest category of expense, also if you plan to do major shopping for high-value items.