This is what I would do if I were you. So you don't go and get yourself into a bad credit card situation and don't do get a lot of inquires going on an application spree.
At BankofAmerica first apply for the Visa Platninum Plus card. If denied they will more than likely offer you either their securd card or their $99/$500 card.( you give them $99 you get a $500 credit line)
I know BankofAmerica does only one credit pull,for all that and I do belive Orchard does as well but not postive. These are the two best options for you out there.
As I said in the earlier post you probably could get an unsecured card from companies like credit one or Aspire but their credit limits are low and they have a ton of fee's and it's not worth at all. As I said before a secured card actually would be a much better option because both orchard bank and Bank of America offer much lower annual fee's Bank of America is a little better because orchard bank charges a $19 processing fee and it's annual fee's vary but they aren't too bad. Bank of America only charges just the $29 annual fee.
so that is what I would do if I were you. I wouldn't go any further than those two cards.