Actually, USAA is a bank. At least the bank part of them is a bank. They're also an insurance company, an investment company, and a few other things. But the banking part is a bank.
From their site's front page: USAA means United Services Automobile Association and its insurance, banking, investment and other companies. Banks Member FDIC. https://www.usaa.com
Online banks like Capital One 360 don't charge overdraft fees and have fast check settlement. I can't comment on transaction ordering or anything - also, it might be hard to find an ATM that will do cash deposits.
And not only is there no account fee, but the checking account pays a pitiable amount of interest.
From their site's front page: USAA means United Services Automobile Association and its insurance, banking, investment and other companies. Banks Member FDIC. https://www.usaa.com
Notice the FDIC. Credit unions are not insured via FDIC, they use NCUA. http://www.gobankingrates.com/banking/fdic-versus-ncua-insur...