Thank you for the data points. We have more information to go on.
I'm guessing you took a hard pull inquiry with Discover, Capital One, and Chase? If so, don't apply anymore without doing some research. Welcome to the myFICO forums.
How many hard pull inquiries have you obtained so far?
Depending on the recency, Discover does offer a secured credit card. They are known to graduate relatively quickly and do soft pull Credit Limit Increases. Perhaps, you should give them a call and see if they can offer a secured card without doing another hard pull, if you did take a hard pull inquiry.
Capital One, I would not recommend the secured card. It will not graduate.
Bank of America, they do offer a secured card. $99 deposit with $500 credit line. I would go in branch and apply for unsecured first. Tell the banker of your limited history. If they do not approve unsecured, the secured card could be offered. BoA graduates quickly and also do soft pull CLI depending on credit profile.