ScotiaBank does at least one account that's free for $3,000 I believe.
RBC does an account that's $4 - with limitations like only 12 transactions a month. You can knock that $4 off to be free if you have a savings and tax-free account with them.
12 transactions includes everything though, so I use them up quick between hydro, gas, insurance, mortgage etc... So I do have to be careful to either not take money out and use my credit card for everything (which is then another one of the 12 transactions to pay off). But it's $1 per transaction extra, their $15 a month account with unlimited transactions wasn't worth it for me, I got like 12 free bank drafts a month ($7.50 each) of which I used 3, ever.
The $15 a month one with RBC also knocks $39 off a credit card, and they do one for $39. It has a lot included but virtually nothing I used. I did get excellent service with a bank manager who would do things like email me stamped documents for free but the one time I wanted one from a branch they charged me $5.
If you go into a bank you can discuss what options you have. But I'd personally start with a minimal one paying nothing/close to and work up if I was to do it again. I spent about $450 with RBC account fees and saved maybe $160. Not worth it, for me.
In terms of credit cards, banks vary. TD declined me because i had a work permit, a friend walked in with a work permit, about to expire, and got $10,000 unsecured.
Most banks, unless you get lucky, will want it secured to start with for at least 6 months. RBC told me the maximum limit on a work permit was $5k, I was well above this before i even got my PR.