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I got in the door in December with a $5k CL Delta Gold revolver... I already met my $1000 spend bonus and got a Seattle/NYC roundtrip flight for $41 after the bonus miles and statement credit.
I didn't think to apply for a charge card. I just googled "easiest Amex to get" and the DG was the card recommended... even with a few threads on these forums.
Ironically I was denied a 31 day CLI... citing my BK13. Will try again in 90 days.
reach for the revolver if you feel you qualify. its not always a cake walk getting the charge card either, but since its less risky to them, the approval criteria is a little looser.