I have Capital One and have not had any issues.
I hear Bank of America is the best though as they actually unsecure the card after a year and give you a nice credit limit increase.
Awful Credit: Public Savings Bank. NO CREDIT CHECK
Bad Credit: Capital One (add unscecured limits and easy to deposit more)
HSBC secured card that has rewards.
Credit union (many have them, not all).
New to Credit: Any major bank that you want to keep doing business with