Where should I put the UPC code? Printed on the product or a sticker on the packaging?

Definitely it should be at packaging as main purpose is to scan and sell the product. otherwise e.g if we are selling at at point of sale then cashier will open the product packaging and then scan to get details of the product which is useless so, never use on product.

Lastly if you have a lot of products you can have separate packaging for each different item and have different upc Code used. i suggest to buy unique cheap UPC codes from below url for multiple different product packaging as each different item will have its own packaging and barcodes.

https://codesforamazon.com/product-category/barcodes/upc-barcodes/