The most realistic materials to reuse for 3d printing would be PET and HIPS. PET is used for all kinds of beverage bottles, and HIPS is used in a lot of packaging.

PLA is not particularly common for product packaging. It exists, but you're not likely to regularly get enough to extrude and spool up. You're more likely to find it in already reusable products like rigid water bottles.

Both grinding input plastic and then extruding that into filament can be challenging to do consistently/well. It also doesn't seem worth the $$ unless you're able to do so at a commercial scale - you run a print farm, you're looking to set up a local(ish) filament recycling scheme, etc.

If you have the time and funds, it does sound like a pretty good rabbit hole to go down.