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If your Credit One has an annual fee or no grace period I would open a Discover Secured and get rid of Credit One. If you are already a member of Navy Fed then I would apply with them after your Cap One is six months old.
To the best of my knowledge Navy Secured cards don't graduate to unsecured, Discover does.
NFCU secured card does graduate.
As the previous poster stated, if the Credit One card has an annual fee, get rid of it.
Also make sure you have some type of installment loan reporting to maximize your score.