I have both. CIBC gave me the newcomer package with no issue. RBC didn't, despite having my CoPR in hand. I would recommend CIBC unless you have the need to transfer funds back to the US.
Yep, as long as they haven't opened an account here. Now on RBC, they have an offer going on till 29 June where they pay 300 CAD into your account subject to the below:
a. Have one payroll deposit before 29 June
b. 2 pre-authorized payments (like mobile phone/home internet etc) before 29 June
The money is then credited into your account within 6 weeks.