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I would say 650+ for the easier cards (Delta SkyMiles, Green), but closer to 700+ for the more difficult cards (Clear, Blue Cash).
I don't think income matters so much, but just be able to prove you have some sort of income via tax returns (*cough* FR *cough*).
Upwards of 700 for bluecash with NO baddies
Upwards of 650 with NO baddies for delta/jet etc