Why do you think you need a separate bank while you are gone? Bank of America has really good online banking. I used them for a long time until they closed all the branches in my area.
At that point, I switched to ING which is now Capital One 360. It's an online only bank and the online banking is excellent. You can deposit checks through a mobile app up to $5K/day. Otherwise you can mail them in. There is also a large ATM network.
Capital One 360 does require that you have a linked land-based checking account. You can use it to deposit checks or cash and then transfer the money.
I would much prefer to get cash at an ATM than cash back at a store. Cash back at a store requires debit card use; I NEVER use a debit card except at the ATM. If someone hacks your debit card, they have access to your bill paying money. If someone hacks your credit card, you cancel the card and the bank deals with it.