I have an OpenSky secured card, no credit check with them.
Open Sky has a $50 annual fee compared to First Progress' $29 (platinum elite), $39 (platinum select), or $44 (platinum prestige) annual fee.
State Department Federal Credit Union has a rewards Visa with no credit check, no annual fee, and 6.99% APR. You have to open an account with them (I opened mine online) and apply for the card via phone.
As you can see below, I have an abysmal score. I've been wanting to open a secured card for the following reasons: 1. I can now control my spending and can use it responsibly, 2. increase my debt to credit ratio, 3. have a card with a good, clean slate. Problem is, I only want to apply ONCE, so I don't have any additional credit checks. Is there a card that has a good acceptance rate for people with as low a score as mine? PS- I have bad history with Barclays, Capital One, and Citi, if that means anything.
I think you need stages of secured cards. First try the sub prime ones that don't pull credit, others have mentioned here. Then after a year or more, you can probably add a secured card from a major bank or credit union. Cap1, USBank, BofA, CITI are all likely to deny at this time, but would be likely after you improve.
US Bank denied me 4 years ago when I started rebuilding and my credit was not nearly as bad. Then I started with Open Sky secured, added HSBC secured at six months, Capital One secured at a year. When secured cards were 1.5 yrs old, I got unsecured cards from the same banks. It takes several years to rebuild.