The following banks and credit unions offer excellent features and benefits. While we recommend them, they are not our top picks for the simple reason that they are not guaranteed banks. They have however helped a lot of people, and may be able to help you too.
Hometown Credit Union
They sometimes use a credit report, otherwise only your ID is required.
Gate City Bank
It has been reported that as long as you do now them any money that they will approve you.
Dakota Plains Federal Credit Union
They run OFAC and TeleCheck to verify new accounts.