Credit score 614.. Should I apply for a credit card now or wait?

I never knew how important your credit was and paid little regard to paying my bills on time when I was younger. I have been repairing my credit for the past 3 years now and have had several loans (2 small personal loans as well as being a cosigner on one vehicle and the single borrower on my car) open and have never been late.

I would like to apply for a credit card but am concerned I'll be turned down and the hit on my credit report will cause negative consequences. I have heard of the secured cards and will get one sometime but am wondering what are my chances of getting an unsecured card? I have a fairly decent ($40,000) income and have been steadily employeed with same company for 3 years.

Would it be okay to apply for a card now or should I continue to wait and let my score get better? It's been steadily improving at a very slow pace!

Thanks!