Do you no longer have the cards in your singature. I'm confused.
With the Cap1, Citi, and First Savings you already have the 3 cards you need to rebuild. Your score will not be helped by a 4th card. (that's just the way the FICO algorithm works).
If you really want a score bump you need a loan. A small secured loan will help. Search the forum for recommended companies. A local credit union is what most people use.
If you did not burn the major banks I would stick with them when going for secured cards to rebuild.
Bank of America and Discover are the other two I would recommend. Discover over BofA. But like I said more cards at this point will not help your score. It will help if you are trying to build a relationship with Discover or BofA.
.... My question is should I go apply ...
You didn't post your Fico scores. How can someone apply without those (among other DPs)?