How do I hide the Category and Brand line on my product pages?

That line comes from the Show Meta setting, which is on by default.

1. Go to Appearance → Catalog Settings.
2. Open the Product Page tab.
3. Untick Show Meta.
4. Click Save Changes.

When it's on, the line shows:

• Category: the product's category, linked to its category page
• Brand: the brand picked in Brand / Vendor on the product

Each part only shows when the product has one, so a product without a brand shows just the category.

The SKU line under the product title is separate and isn't controlled by Show Meta. The setting applies to every product using the standard product page layout.