Thanks for the help!
In order:
1. Chase's chip card is Chip+Sign only, no PIN. It's also got a high annual fee. Same with US Bank, and while I already bank with Wells Fargo in the US, they're telling me that their chip card is a closed trial right now.
2. A Canadian mailing address I can do. My sister's studying at UBC and when I visit I'll be staying/picking up my mail at her place (apartment, not dorm room). Also, I already noticed the lack of Visa debit cards (I know about CIBC, but they want a $4 monthly fee for a basic checking account with 10 transactions/month- not very appealing) so that's why I was asking about savings account+credit card first. I'll keep that in mind about not being able to get an unsecured card and ask about a secured card also.
Though the weird thing about CIBC was that since I posted this, I accompanied my sister to her account opening (she's a student so she gets a checking account with unlimited transactions for free- lucky). The lady promoting credit cards at the branch said that they could pull up my US history and even send the card to my American address if I got approved. Is she just desperate for a commission, misinformed, or are they that American-friendly?
3. Thanks for the advice, I'll give RBC a look too. Truth be told, the first time I didn't give them a second look because I was silly and assumed the Avion card was the only one they offered (because that seems to be the only card they ever advertise).
I've already left and I won't be back for a while, but it looks like my first course of action would be like this:
Head to RBC, ask about getting a credit card. Probably going to get a GIC too if it gets approved, then I get the fee waived on a basic checking account (multi-product rebate).
If that fails, then I'll head to CIBC. Apply for a credit card, and if that passes, get a savings account there to pay the bill with.
And if that fails, I'll go back and ask about secured cards and try again.
Also, as for "all banks"- some insist on residency. Scotiabank told me they wouldn't without proof of a long-term visa, Coast Capital insisted on an SIN, and I guess I haven't tried that many others. It'd be easier if they'd take a phone bill or something as "proof of residency"- I managed to get a Rogers postpaid plan with just my American passport and CC that shows my sister's address and already have bills for that. Oh well.