I made use of Scotia StartRight program for permanent residents.
3 days after I landed, I was able to open a powerchequing account (no fees for 1 year), moneymaster savings and was approved for a No fee Visa credit card with $1,000 limit. They did not ask for security deposit, and I did not have a job then as well.
Most banks have a newcomer program, just depends on your preference which one you will bank with.