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I would say at least 620.
Search for the credit pulls database and the answer to your question will be there as you'll be able to see the scores of people that were approved and denied for the card(s) you are considering.
I was around 620 when I got mine. I think your TU is a little low (both Target and WM pulled TU for me).
What's your utilization currently? If you're over 10% you may be getting dinged a little there and paying down your balances could bring your TU up over 600. Otherwise, if you give it a few months you should be in a better spot to app for one or both.
Is target card a different bank than it was in the past? I burned them previously about 7-10 years ago.
Is Walmart inquiry sensitive?
Kohls will give you a card. I got denied by both Walmart and Target with scores like yours and nothing bad in 4 years and six figure annual income. Really by the time you can get a card from either of them why would you want one.