When I first got here, I opened an account with Chase bank. It was ok until i tried to get a credit card and they wouldn't even give a guaranteed card..so I closed my account with them and Capital One welcomed me with a $300 credit line which I used to build my credit and after 6 month they increased the limit to $1500. When you are new, most banks don't want to touch you but after a while and you have a bit of credit history, they all start sending you unsolicited credit cards. So Capital One or small Credit Unions in your area should sort you out.