Bank Of China! Stay away from rest for less hassle.
I opened account, internet banking, Phone banking, credit/deposit card with Bank Of China effortless when i got here. If you search online you might find some references saying BOC requires foreigners a minimum deposit of 500us$ to open an account. In my case they did not ask any deposit at all.
About deposit box, im not sure they even have. I never saw and my gf says neither did she.