I'd do the unsecured (even though Credit One is a high-fee, low CL card). Wait for that to report on all 3 CRAs, then app for a secured.
By waiting, you'll likely get a score bump across all 3. And if I could do it all over again, besides waiting, I would have saved more. My bank had offered me a secured CC for $2k if I would deposit that first in a CD for 1 yr. Had I done that, subsequent approvals would have resulted in CLs of $1000 plus versus these $300-$600 CLs I have now. In other words, save more than the $500 and get a secured card in a couple months. Make sure the lender will convert the card to an unsecured in about a year's time (unlike Orchard, e.g.).
Also, secured cards aren't that bad. Lenders, like my bank, mentioned that it was a favorable thing to see. Not too many people in financial distress proactively save, yet alone save for a CC deposit.