Some popular ways to do PK: natural key, sequentially generated key, and UUID. Personally I would prefer natural key if I can find an immutable natural key for the table. However, natural keys are hard to find. The food example in this case doesn't have natural key. Also if the natural key requires a compound key, it's just not worth the pain.
Sequential auto generated key is good when you need to hand it off to users, like order id or ticket number. It's short and simple and it's auto generated. The downsize is when you migrate databases, you need to seed the new database carefully or it would start from beginning again. Also in record creation, you need to do extra read to get back the newly generated key.
UUID is mostly worry free. It can be generated anywhere and doesn't need to be in the database. For a setup with distributed databases, I would use UUID just to have global uniqueness. For an offline app, I would use UUID to create the data records locally and later sync them with the main database. UUID is good when it's used internally and not exposed to the users.