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Do you know your FICO scores?
If your TU is at least 590 you might have a chance. I did with no CCs at all to speak of. You will probably have a low CL, but hey free TU score.
You won't qualify for either and will waste a hard pull. If your fako is 600, my guess is your real FICO is somewhere in the 550's.
You could definitely try, but in my experience having a few collections like that will impact you. For me, I couldn't even get a Macy's card when I had just 2 collections on my acct that were 5 years old. Tell me about your Authorized User stuff, that may get you qualified if it's a high enough amount (2000+) and for a long period of time.
They are both underwritten by GECRB so you have an equal chance of getting either one. I think you have a better chance of getting Walmart however out of the two.
JCP and Walmart will pull TU. IMO, your scores should be around 620.
YMMV
For me, Walmart pulled Experian. It really depends on where in the country you are that will dictate the bureau they use for the pull.