When is the earliest that I can try to re-apply for another credit card without it lowering my credit score?

I just closed a/my first credit card account because I was told that it would not lower my credit score. And now I am wondering when is the earliest that I can try to reapply for another credit card without it lowering my credit score. And if I didn’t/don’t have to wait, I saw/see that Citi has a platinum select card with a standard purchase apr of as low as 6.74% and Nordstrom has a visa signature card with a many levels of apr depending on your credit. They range from prime rate plus zero, 3.9%, 6.9%, 10.9% and 14.9%. Which would be a better deal for me?
Please answer my main/first question that is: When is the earliest that I can try to re-apply for another credit card without it lowering my credit score?

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