The distinction that causes expensive mistakes is between a genuine identifier and a printed code. Retail barcodes are numbers registered to your company through the global standards organisation, and the registration is what retailers verify. There is a resale market offering the same numbers far more cheaply, and those numbers are typically registered to somebody else. Major retailers and marketplaces check, and a product with a number registered to another company gets rejected, sometimes after you have already manufactured packaging.
For your own operations, none of that applies. Internal codes for tracking your own stock can be anything you generate yourself, free, using whatever your inventory system produces. If the purpose is scanning items in your own shop or warehouse rather than selling through somebody else, generate them and move on.
The practical sequence is to decide your sales channels before ordering packaging. If wholesale or marketplace selling is plausible within a year, register properly at the outset, because retrofitting identifiers onto printed packaging is the expensive version of this decision. If you are certain you will only ever sell directly, skip it and revisit if the plan changes.
One detail worth knowing: each distinct variant needs its own identifier. A shirt in three colours and four sizes is twelve products by this definition, not one, and pricing for registration is generally tiered by how many you need. Work out that number before you look at the cost, because the naive estimate is usually wrong by an order of magnitude.
Order the identifiers before the packaging design is finalised rather than afterward, because the code needs physical space, a quiet margin around it, and adequate contrast to scan reliably. Designers who receive the requirement late frequently place it somewhere that scans poorly, and the discovery happens at a retailer rather than in your workshop. Print a test at actual size and scan it with an ordinary phone before committing to a print run.
Keep a register of which identifier belongs to which product variant, maintained as you add products. This sounds trivial with four products and becomes genuinely difficult with forty across sizes and colours, and a mistake means a retailer receiving the wrong item against a scanned code. The register also matters when you eventually sell through a channel that verifies your registration, since you will be asked to confirm exactly what each number refers to.