For what it's worth, the Goodyear credit card offer OP is describing (most likely) applies to GY tires purchased at TireRack too. For me it was a $75 base manufacturer mail-in-rebate which was bumped up to $150 if I had the goodyear credit card. Not worth burning a credit card slot for $75, obviously, so I just took the base mail-in-rebate.

+1 on buying online and having the tires shipped to an independent installer though. Much cheaper than the dealer and better service than the big shops i.e. Firestone/Discount Tire/Pepboys

What do you envision paying with your checking account? It's one thing if your study abroad is in a developing/cash-based economy, but if for example it's somewhere in Europe or most of Asia you can use a credit card for 99% of transactions. It's of course nice to have a small amount of cash on hand, but in amounts that a 3% transaction fee isn't worth the hassle of setting up a new account.

I would recommend using a 0% FTF credit card if you can. The extra layer of protection offered by the credit card is very helpful when you're in a foreign country and have a higher likelihood of getting scammed or having the card be lost/stolen. Assuming you'll be traveling during the downtime between classes, the insurance on rental cars, plane/train tickets, lost luggage, etc. may come in handy too.

There's tons of 0% FTF cards with no annual fee but Capital One and the Amazon Prime card come to mind if you don't have an extensive credit history yet.

If your credit is actually zero I think it's unlikely you'll be approved for a co-branded airline card from a major bank or have high enough of a credit limit to purchase international flight tickets on. That said, it's a great idea to use a credit card for the trip since many offer 0% foreign transaction fee and another layer of purchase protection.

I personally prefer straight cash back cards instead of airline cards since it doesn't lock you in to a particular company and it's easier to get rewards when you want it, but it's ultimately up to you.