Which HS code applies to retail-ready private label goods?

Confidence 4/5 Established practice

HS classification for retail-ready private label goods:

Follows the product, not the brand. A private-label item is classified exactly as the unbranded equivalent.

Private label and OEM practice — Industry practice; consistent with supplier-quoted minimums
Country of origin marking requirements — US Customs and Border Protection
EU product labelling and responsible person requirements — European Commission

What goes wrong with retail-ready private label goods

Printing the packaging before confirming the destination labelling requirement, then paying for a reprint.
Assuming the factory will generate the barcode. GS1 registration is the brand owner's job.
Buying a "custom" product that is actually a stock item with a sticker on it — sometimes fine, but you should know which you bought.
Forgetting the responsible-person address required for EU sales.
Not checking that the factory will not also supply your design to someone else; exclusivity has to be negotiated and paid for.

Send the requirement and any drawings. You get a supplier shortlist and one landed price, with the cost breakdown shown.