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.
Northern Lights Credit Union
They use ChexSystems but anyone can get a savings account.
White River Credit Union
They do not use any verification systems but they do reserve the right to run a credit report on you.