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At one year your inquiries for the cards you have will not effect your Fico score. That and lowering your utilization <9% will have a positive effect for getting a card. If I were you I would wait until then to apply for anything. IMHO
IMO you have done well and I know its hard to wait but that being said wait until scores hit mid 600's
I can't think of many (non-shark) lenders that would be 600 friendly. Perhaps Barclaycard and BankofAmerica (the BOA is likely to deny for unsecured but may counter with the 99/500 secured card, which is very good rebuilder card because it becomes eligible to unsecure). But neither of those pull EQ (or only EQ).
It may serve you better to not add any new cards at all--just keep working on establishing your AAOA, UTL and raise that FICO to 640 before you app.
If you are okay with secured cards, get the BofA secured card when your scores are at 600. The downside is that it's a secured card so you will have to come up with the deposit, but what's nice is that BofA usually graduate customers pretty easily after 6-12 months.