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.
Pine Creek Federal Credit Union
They do not offer checking accounts. They only offer savings and you must be eligible for membership to open a savings.
They do sometimes open accounts for those reported to ChexSystems depending on the severity of the report.